{"id":45,"date":"2023-09-17T10:57:01","date_gmt":"2023-09-17T10:57:01","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/"},"modified":"2023-09-17T10:57:01","modified_gmt":"2023-09-17T10:57:01","slug":"%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/","title":{"rendered":"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u044d\u0442\u0430\u043f\u043d\u043e \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438, \u0440\u0435\u0448\u0430\u044e\u0449\u0438\u043c\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-problemas-de-optimizacion\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0417\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438<\/strong> \u2014 \u044d\u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043d\u0430\u0439\u0442\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u043c\u043e\u0436\u0435\u0442 \u0432\u043a\u043b\u044e\u0447\u0430\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0449\u0435\u0439 \u043f\u0440\u0438\u0431\u044b\u043b\u044c \u043a\u043e\u043c\u043f\u0430\u043d\u0438\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-resolver-los-problemas-de-optimizacion\"><\/span> \u041a\u0430\u043a \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u043f\u043e \u0443\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0431\u043b\u0435\u043c \u0441 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0439:<\/p>\n<ol>\n<li> <strong>\u0423\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e<\/strong> , \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/li>\n<li> <strong>\u0412\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/strong><\/li>\n<li> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 <strong>\u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u044f\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0443\u043b\u044e \u0438 \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.<\/li>\n<li> \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 <strong>\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-problema-de-optimizacion\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0420\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044f \u0442\u0435\u043e\u0440\u0438\u044e \u0437\u0430\u0434\u0430\u0447 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u043f\u043e\u044d\u0442\u0430\u043f\u043d\u043e \u0440\u0435\u0448\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0438 \u0442\u0430\u043a\u043e\u0433\u043e \u0442\u0438\u043f\u0430, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u043e\u043d\u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044e\u0442\u0441\u044f.<\/p>\n<ul>\n<li> \u0421\u0440\u0435\u0434\u0438 \u0432\u0441\u0435\u0445 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0445 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432, \u043e\u0431\u0449\u0430\u044f \u0434\u043b\u0438\u043d\u0430 \u043a\u0430\u0442\u0435\u0442\u043e\u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0440\u0430\u0432\u043d\u0430 10 \u0441\u043c, \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u044b \u0442\u043e\u0433\u043e, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0430\u044f.<\/li>\n<\/ul>\n<p> \u0414\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430\u0437\u043e\u0432\u0435\u043c \u043e\u0434\u043d\u0443 \u0432\u0435\u0442\u0432\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 <em>x<\/em> , \u0430 \u0434\u0440\u0443\u0433\u0443\u044e \u0432\u0435\u0442\u0432\u044c <em>y<\/em> : <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-optimisation-probleme.webp\" alt=\"\u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430\" class=\"wp-image-2463\" width=\"172\" height=\"156\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> <u style=\"text-decoration-color:#FF9B28;\"><strong><span style=\"color:#1976d2;\">\u0428\u0430\u0433 1:<\/span><\/strong> \u0423\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/u><\/p>\n<p> \u041c\u044b \u0445\u043e\u0442\u0438\u043c, \u0447\u0442\u043e\u0431\u044b \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0431\u044b\u043b\u0430 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0439, \u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0442\u0430\u043a\u0430\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d1fe72037bfa7f8a181f8f92fdeb5a93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A = \\cfrac{b \\cdot h}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"70\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0412 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u2014 <em>x<\/em> , \u0430 \u0435\u0433\u043e \u0432\u044b\u0441\u043e\u0442\u0430 <em>\u2014 y<\/em> . \u0415\u0449\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fffb2f09f07fa450174fda22346dc38d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A = \\cfrac{x \\cdot y}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"72\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0423 \u043d\u0430\u0441 \u0443\u0436\u0435 \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u043b\u044f \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u043d\u043e \u043e\u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0434\u0432\u0443\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u0442\u043e\u0433\u0434\u0430 \u043a\u0430\u043a \u043c\u043e\u0436\u0435\u0442 \u0437\u0430\u0432\u0438\u0441\u0435\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u043e\u0434\u043d\u043e\u0439. \u041e\u0434\u043d\u0430\u043a\u043e \u0432 \u0437\u0430\u044f\u0432\u043b\u0435\u043d\u0438\u0438 \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u0441\u044f, \u0447\u0442\u043e \u043e\u0431\u0449\u0430\u044f \u0434\u043b\u0438\u043d\u0430 \u0434\u0432\u0443\u0445 \u043d\u043e\u0433 \u0434\u043e\u043b\u0436\u043d\u0430 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0442\u044c 10 \u0441\u043c. \u0415\u0449\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97009913e60b18a66b47683b142eaa14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+ y = 10\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0420\u0435\u0448\u0430\u0435\u043c \u0434\u043b\u044f <em>y<\/em> \u0438\u0437 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9093174098ec3aeadce1fa9dd3724c27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 10 -x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0418 \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u044e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9ab3460a669f3a70a608b0a4c64f520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A = \\cfrac{x \\cdot y}{2} \\ \\xrightarrow{ y \\  = \\ 10 -x } \\ A = \\cfrac{x(10-x)}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"278\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-28b512042d814bf88207c8fb0f9a5543_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x) = \\cfrac{10x-x^2}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"131\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0437\u0430\u043f\u043b\u0430\u043d\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u0438 \u043e\u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u043e\u0434\u043d\u043e\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043a \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u0448\u0430\u0433\u0443.<\/p>\n<p> <u style=\"text-decoration-color:#FF9B28;\"><strong><span style=\"color:#1976d2;\">\u0428\u0430\u0433 2:<\/span><\/strong> \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438.<\/u><\/p>\n<p> \u042d\u0442\u043e \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0435\u0435 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043e\u0442 \u0434\u0435\u043b\u0435\u043d\u0438\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d555f298d7c31d09947787e4d294d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x) = \\cfrac{10x-x^2}{2} \\ \\longrightarrow \\ A'(x) = \\cfrac{(10-2x) \\cdot 2 - (10x-x^2) \\cdot 0}{2^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"467\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00979b72662361213ec4611a28e935a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x) = \\cfrac{20-4x}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"126\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> <u style=\"text-decoration-color:#FF9B28;\"><strong><span style=\"color:#1976d2;\">\u0428\u0430\u0433 3:<\/span><\/strong> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438.<\/u><\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u044f\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043d\u0443\u043b\u044e \u0438 \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91e81f70cf7bd6388f6511629d203f7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5753c4fdb7aaae61182eac6fd15e52d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{20-4x}{4} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"91\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> 4 \u0434\u0435\u043b\u0438\u0442 \u0432\u0441\u044e \u043b\u0435\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0438\u0442\u044c \u0435\u0435, \u0443\u043c\u043d\u043e\u0436\u0438\u0432 \u0432\u0441\u044e \u043f\u0440\u0430\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23e63171262e022c8a63e717b31ed0b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"20-4x=0 \\cdot 4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"113\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e9b9b9a13bafb9de785e9cf5b3e86ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"20-4x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"91\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e71409a99fca0883bc173a6df1b8c3af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-4x=-20\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"87\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-66b399752305ae60043d99032ba112d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-20}{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <u style=\"text-decoration-color:#FF9B28;\"><span style=\"color:#1976d2;\"><strong>\u0428\u0430\u0433 4:<\/strong><\/span> \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/u><\/p>\n<p> \u0414\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u0443\u044e \u0441\u043f\u0440\u0430\u0432\u0430: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-5.webp\" alt=\"\" class=\"wp-image-2466\" width=\"227\" height=\"88\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043e\u0446\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u0438\u043b\u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (\u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443) \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00979b72662361213ec4611a28e935a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x) = \\cfrac{20-4x}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"126\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9c9fbc0304871964748873af9e9918c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(0) = \\cfrac{20-4\\cdot0}{4} = \\cfrac{20}{4} = 5  \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"264\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05c98faeaeb88c5826a71a45b3e9c88a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(6) = \\cfrac{20-4\\cdot6}{4} = \\cfrac{20-24}{4} = \\cfrac{-4}{4} = -1   \\  \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"373\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-5-positif-negatif.webp\" alt=\"\" class=\"wp-image-2467\" width=\"227\" height=\"160\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442, \u0430 \u0435\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0431\u044b\u0432\u0430\u0435\u0442. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0443\u0432\u0435\u043b\u0438\u0447\u0435\u043d\u0438\u044f \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0420\u043e\u0441\u0442:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-188a50f6279237f5c478c7116a509d49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty, 5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0421\u043d\u0438\u0436\u0430\u0442\u044c\u0441\u044f:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-743f877080ce04389168296915ca6795_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(5,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u0438 x=5 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u043a \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=5 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 <strong>.<\/strong><\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, x=5 \u2014 \u044d\u0442\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0442\u043e\u0439 \u0432\u0435\u0442\u0432\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438\u043c\u0435\u0435\u0442 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u043f\u043b\u043e\u0449\u0430\u0434\u044c. \u041f\u0440\u043e\u0441\u0442\u043e \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c \u0434\u0440\u0443\u0433\u043e\u0439 \u043d\u043e\u0433\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d396031e1a0eb65570a9f95d6701f9c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 10 -x \\ \\xrightarrow{x \\ = \\ 5} \\ y = 10-5= \\bm{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"265\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0412 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u044e\u0442 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-85b25208de94c730a3de04d6d428dc59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=5} \\ \\mathbf{cm}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"75\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e7e41736bd949777d18ec2a79b0beb93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=5} \\ \\mathbf{cm}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"problemas-de-optimizacion-resueltos\"><\/span> \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u0441 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0435\u0439 \u0440\u0435\u0448\u0435\u043d\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 1<\/h3>\n<p> \u041b\u0435\u043a\u0430\u0440\u0441\u0442\u0432\u043e \u0434\u0430\u044e\u0442 \u0431\u043e\u043b\u044c\u043d\u043e\u043c\u0443 \u0438<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0447\u0435\u0440\u0435\u0437 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0447\u0430\u0441\u043e\u0432 \u043a\u043e\u043d\u0446\u0435\u043d\u0442\u0440\u0430\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u0438\u043d\u0433\u0440\u0435\u0434\u0438\u0435\u043d\u0442\u0430 \u0432 \u043a\u0440\u043e\u0432\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57f138f86e1400954205e4b91ed3103c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c(t) = te^{\u2212t\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u043c\u0438\u043b\u043b\u0438\u0433\u0440\u0430\u043c\u043c\u044b \u043d\u0430 \u043c\u0438\u043b\u043b\u0438\u043b\u0438\u0442\u0440. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4be04707471a329c8bde249ab6cf526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c(t)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0438 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u043a\u043e\u0433\u0434\u0430 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442\u043e. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 1: \u0423\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435 \u043d\u0430\u043c \u0443\u0436\u0435 \u0434\u0430\u044e\u0442 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0435\u0441\u0442\u044c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02fb8044e28a7e9ba53c1eb64bfec693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle c(t) = t e^{-t\/2} .\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"100\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 2: \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1975d832fe40c4c12a2a4986244e3c24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle c'(t)=1 \\cdot e^{-t\/2} + t \\cdot e^{-t\/2} \\cdot \\left( \\frac{-t}{2} \\right)'= e^{-t\/2} + t e^{-t\/2} \\cdot  \\frac{-1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"430\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d730042a2ff5df46d19bce35fe24392_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c'(t)=e^{-t\/2} + \\cfrac{-1}{2}t  e^{-t\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"193\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 3: \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0440\u0435\u0448\u0430\u0435\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-626f673c4823e1bd527925bfe91d558f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c'(t)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64818981c87104d6e0b400434ce53533_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c'(t)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d9ebad9fa6bc78dc99b358f4786999f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle e^{-t\/2} + \\frac{-1}{2}t  e^{-t\/2}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"164\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432\u043e\u0437\u044c\u043c\u0435\u043c \u043e\u0431\u0449\u0438\u0439 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u044c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-410004b26bf5de6dc03c12491bee91b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle e^{-t\/2} \\left(1 - \\frac{1}{2}t \\right) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"150\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0431\u044b\u043b\u043e \u0440\u0430\u0432\u043d\u043e 0, \u043e\u0434\u0438\u043d \u0438\u0437 \u0434\u0432\u0443\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u043d\u0443\u043b\u0435\u043c. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0443\u0441\u0442\u0430\u043d\u0430\u0432\u043b\u0438\u0432\u0430\u0435\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0444\u0430\u043a\u0442\u043e\u0440 \u0440\u0430\u0432\u043d\u044b\u043c 0:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8390139724dbc4ad014db2a76e508290_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle e^{-t\/2}\\cdot \\left(1 - \\frac{1}{2}t \\right) = 0 \\longrightarrow \\begin{cases} e^{-t\/2}=0 \\ \\bm{\\times} \\\\[2ex]\\displaystyle 1 - \\frac{1}{2}t=0 \\ \\longrightarrow \\ 1= \\frac{1}{2}t \\ \\longrightarrow \\ \\bm{2=t} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"486\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0427\u0438\u0441\u043b\u043e, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0435 \u0432 \u0434\u0440\u0443\u0433\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0434\u0430\u0442\u044c 0, \u043f\u043e\u044d\u0442\u043e\u043c\u0443<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10b6a1e4b24bf63d08aeff4da0374d25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e^{-t\/2}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0435\u0442.<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 4: \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0414\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u0443\u044e \u0441\u043f\u0440\u0430\u0432\u0430: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-2.webp\" alt=\"\" class=\"wp-image-2469\" width=\"204\" height=\"79\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043e\u0446\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u0438\u043b\u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (\u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443) \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-904d140578309f45e9c53d2a9a35e32d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle c'(0)=e^{-0\/2} + \\frac{-1}{2}\\cdot 0 \\cdot e^{-0\/2} = e^0 +\\frac{-1}{2}\\cdot 0 \\cdot e^{0} = 1 + 0 = 1 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"508\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ada4b79153afee560564a81df8d0c46f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle c'(3)=e^{-3\/2} + \\frac{-1}{2}(3)e^{-3\/2} = 0,22-0,33 = -0,11 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"449\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-deux-positif-negatif.webp\" alt=\"\" class=\"wp-image-2472\" width=\"202\" height=\"143\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0432\u0430\u0435\u0442\u0441\u044f, \u0430 \u0435\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0431\u044b\u0432\u0430\u0435\u0442. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0440\u043e\u0441\u0442\u0430 \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u043c\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0420\u043e\u0441\u0442:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3868632c123ece40100b3a40c266cc25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0421\u043d\u0438\u0436\u0430\u0442\u044c\u0441\u044f:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c9901d11cc4672cab7e1e2a6de08ce4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u043a \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044e \u043f\u0440\u0438 t=2, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>t=2 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0430\u044f \u043a\u043e\u043d\u0446\u0435\u043d\u0442\u0440\u0430\u0446\u0438\u044f \u0431\u0443\u0434\u0435\u0442 \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442\u0430 \u0447\u0435\u0440\u0435\u0437 <strong>t=2 \u0447\u0430\u0441\u0430.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c, \u0432 \u0438\u0441\u0445\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u043a\u043e\u043d\u0446\u0435\u043d\u0442\u0440\u0430\u0446\u0438\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd8123e6fd3fe714d1784775375011f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c(2) = 2 \\cdot e^{-2\/2} = 2\\cdot e^{-1} = 2 \\cdot 0,37 = \\bm{0,74} \\ \\mathbf{mg\/ml}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"391\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 2<\/h3>\n<p> \u041e\u0434\u0438\u043d \u043c\u0430\u0433\u0430\u0437\u0438\u043d \u043d\u0430\u0434\u0435\u0435\u0442\u0441\u044f \u043f\u0440\u043e\u0434\u0430\u0442\u044c 40 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u0441\u0430\u043c\u043e\u043a\u0430\u0442\u043e\u0432 \u043f\u043e \u0446\u0435\u043d\u0435 1000 \u0435\u0432\u0440\u043e \u0437\u0430 \u0441\u043a\u0443\u0442\u0435\u0440. \u041d\u043e \u0441\u043e\u0433\u043b\u0430\u0441\u043d\u043e \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f\u043c \u0440\u044b\u043d\u043a\u0430, \u043d\u0430 \u043a\u0430\u0436\u0434\u044b\u0435 50 \u0435\u0432\u0440\u043e \u0441\u043d\u0438\u0436\u0435\u043d\u0438\u044f \u0446\u0435\u043d\u044b \u0441\u043a\u0443\u0442\u0435\u0440\u0430 \u043f\u0440\u043e\u0438\u0437\u043e\u0439\u0434\u0435\u0442 \u0443\u0432\u0435\u043b\u0438\u0447\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0434\u0430\u0436 10 \u0441\u0430\u043c\u044b\u0445 \u043f\u0440\u043e\u0434\u0430\u0432\u0430\u0435\u043c\u044b\u0445 \u0441\u043a\u0443\u0442\u0435\u0440\u043e\u0432.<\/p>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u043f\u0438\u0448\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0434\u043e\u0445\u043e\u0434\u0430 \u043c\u0430\u0433\u0430\u0437\u0438\u043d\u0430, \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u043d\u0443\u044e \u043d\u0430 \u0442\u043e\u043c, \u0432\u043e \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0437 \u043f\u0435\u0440\u0432\u043e\u043d\u0430\u0447\u0430\u043b\u044c\u043d\u0430\u044f \u0446\u0435\u043d\u0430 \u0441\u0430\u043c\u043e\u043a\u0430\u0442\u0430 \u0432 1000 \u0434\u043e\u043b\u043b\u0430\u0440\u043e\u0432 \u0443\u043c\u0435\u043d\u044c\u0448\u0438\u043b\u0430\u0441\u044c \u043d\u0430 50 \u0434\u043e\u043b\u043b\u0430\u0440\u043e\u0432. \u0417\u0430\u0442\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0446\u0435\u043d\u0443 \u0441\u0430\u043c\u043e\u043a\u0430\u0442\u0430, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u043f\u0440\u0438\u0431\u044b\u043b\u044c \u0438 \u0434\u043e\u0445\u043e\u0434, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0439 \u043f\u043e \u044d\u0442\u043e\u0439 \u0446\u0435\u043d\u0435. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 1: \u0423\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u0430\u0435\u0442 \u043d\u0430\u043c \u043f\u043e\u0434\u0441\u043a\u0430\u0437\u043a\u0443, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0433\u043e\u0432\u043e\u0440\u0438\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u043e\u043b\u0436\u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0435\u0442\u044c \u043e\u0442 \u0442\u043e\u0433\u043e, \u0432\u043e \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0437 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u0430\u044f \u0446\u0435\u043d\u0430 \u0443\u043c\u0435\u043d\u044c\u0448\u0438\u043b\u0430\u0441\u044c \u043d\u0430 50 \u0434\u043e\u043b\u043b\u0430\u0440\u043e\u0432. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043d\u0430\u0437\u043e\u0432\u0435\u043c x \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0440\u0430\u0437, \u043a\u043e\u0433\u0434\u0430 \u0446\u0435\u043d\u0430 \u0441\u043d\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043d\u0430 50 \u0435\u0432\u0440\u043e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d0357e75c58ab161e387dae18d3a6f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= \\text{N\\'umero de veces que se rebaja el precio 50}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"368\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u20ac<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u043e\u0445\u043e\u0434\u0430 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u043d\u0430 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0443 \u043f\u0440\u043e\u0434\u0430\u043d\u043d\u044b\u0445 \u0441\u043a\u0443\u0442\u0435\u0440\u043e\u0432, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u043c\u0443 \u043d\u0430 \u0446\u0435\u043d\u0443 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0441\u043a\u0443\u0442\u0435\u0440\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f04d6d19de5d7a7ad8dceadfbbdbdbe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= \\text{N\\'umero patintetes vendidos} \\cdot \\text{Precio de cada patinete}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"470\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u0440\u043e\u0434\u0430\u043d\u043d\u044b\u0445 \u0441\u0430\u043c\u043e\u043a\u0430\u0442\u043e\u0432 \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u0442 40 \u043f\u043b\u044e\u0441 10 \u0441\u0430\u043c\u043e\u043a\u0430\u0442\u043e\u0432 \u0437\u0430 \u043a\u0430\u0436\u0434\u044b\u0435 50 \u0435\u0432\u0440\u043e \u0441\u043d\u0438\u0436\u0435\u043d\u0438\u044f \u0446\u0435\u043d\u044b. \u0415\u0449\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88b7464372c9683d065acbdbe2598cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{N\\'umero patintetes vendidos} = 40 + 10x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"308\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0426\u0435\u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0441\u0430\u043c\u043e\u043a\u0430\u0442\u0430 \u043d\u0430 \u0441\u0442\u0430\u0440\u0442\u0435 \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u0442 1000 \u0435\u0432\u0440\u043e \u0438 \u0431\u0443\u0434\u0435\u0442 \u0441\u043d\u0438\u0436\u0430\u0442\u044c\u0441\u044f \u043d\u0430 50 \u0435\u0432\u0440\u043e \u0441 \u043a\u0430\u0436\u0434\u044b\u043c \u0441\u043d\u0438\u0436\u0435\u043d\u0438\u0435\u043c \u0446\u0435\u043d\u044b. \u0415\u0449\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c22a7a64d350ea748ad2b4b3decd217_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Precio de cada patinete} = 1000 -50x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"291\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0442\u0430\u043a\u043e\u0432\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f04d6d19de5d7a7ad8dceadfbbdbdbe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= \\text{N\\'umero patintetes vendidos} \\cdot \\text{Precio de cada patinete}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"470\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2cbffd131757d106f869b562d4e35c4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= (40 + 10x) \\cdot (1000-50x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"249\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ae987678d7542e5d127fc02f8bf4daf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= 40000-2000x+10000x-500x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-902cc0a5c209ed48e3d93432b5550b1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= -500x^2+8000x+40000\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"249\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 2: \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u0435\u0435 \u043b\u0435\u0433\u0447\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acb8d705be4d3a30be83d2800f4d2403_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= -500x^2+8000x+40000\\ \\longrightarrow \\ I'(x)= -1000x+8000\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"477\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 3: \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0440\u0435\u0448\u0430\u0435\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b55b4fb6ca5af90f829cb082893a5519_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8b48142b0c92fea1f9dd87af211ada6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a0d58fd339d02e3f71b7fe031726cad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1000x+8000=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"148\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a03bae4e019041d174c51fced30954ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1000x=-8000\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"132\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e67f8bf53c9c10c3384f729890f57b4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-8000}{-1000} = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"125\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 4: \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0414\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u0443\u044e \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u043d\u0430 \u0447\u0438\u0441\u043b\u043e\u0432\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-8.webp\" alt=\"\" class=\"wp-image-2481\" width=\"234\" height=\"91\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043e\u0446\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u0438\u043b\u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (\u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443) \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3cf47c71ae832d734c6e5f525efa05b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I'(0)= -1000\\cdot 0+8000=8000 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"300\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9df9f5fdff3d4ba6dcd7f17c68b16c2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I'(10)= -1000\\cdot 10+8000=-2000 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"331\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-8-positif-negatif.webp\" alt=\"\" class=\"wp-image-2482\" width=\"239\" height=\"169\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442, \u0430 \u0435\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0431\u044b\u0432\u0430\u0435\u0442. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0440\u043e\u0441\u0442\u0430 \u0438 \u043f\u0430\u0434\u0435\u043d\u0438\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0420\u043e\u0441\u0442:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d85d36c78a812c7c5a8f127bb5145c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,8)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0421\u043d\u0438\u0436\u0430\u0442\u044c\u0441\u044f:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ba6980946255650ee8fe4dbc4c87c681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(8,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u043a \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044e \u043f\u0440\u0438 x=8, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=8 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0434\u043e\u0445\u043e\u0434 \u0431\u0443\u0434\u0435\u0442 \u043f\u043e\u043b\u0443\u0447\u0435\u043d, \u0435\u0441\u043b\u0438 \u0441\u0434\u0435\u043b\u0430\u0442\u044c <strong>\u0441\u043a\u0438\u0434\u043a\u0443 \u0432 50 \u0435\u0432\u0440\u043e \u0432 8 \u0440\u0430\u0437.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u043f\u043e\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0434\u043e\u0445\u043e\u0434, \u0432 \u0438\u0441\u0445\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0434\u043e\u0445\u043e\u0434\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-902cc0a5c209ed48e3d93432b5550b1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= -500x^2+8000x+40000\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"249\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fce0d14898ab44824c50e758de24099d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(8)= -500\\cdot 8^2+8000\\cdot 8+40000 = \\bm{72000}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"339\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>\u20ac<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0446\u0435\u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0441\u0430\u043c\u043e\u043a\u0430\u0442\u0430 \u043f\u043e\u0441\u043b\u0435 8-\u043a\u0440\u0430\u0442\u043d\u043e\u0439 \u0441\u043a\u0438\u0434\u043a\u0438 \u0432 50 \u0435\u0432\u0440\u043e \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c22a7a64d350ea748ad2b4b3decd217_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Precio de cada patinete} = 1000 -50x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"291\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a4646c3d785d36e70ba549b9672b697c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Precio de cada patinete} = 1000 -50\\cdot 8=\\bm{600}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"353\" style=\"vertical-align: -4px;\"><\/p>\n<p> <strong>\u20ac<\/strong><\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 3<\/h3>\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u044e \u0437\u0430\u0442\u0440\u0430\u0442 (\u0432 \u0442\u044b\u0441\u044f\u0447\u0430\u0445 \u0435\u0432\u0440\u043e) \u043a\u043e\u043c\u043f\u0430\u043d\u0438\u0438 \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c84c0900acd506ad979886e5b5f10ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=40-6x+x^2, \\quad x \\ge  0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"224\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0417\u043e\u043b\u043e\u0442\u043e<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0442\u044b\u0441\u044f\u0447\u0438 \u0435\u0434\u0438\u043d\u0438\u0446, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u043e\u0433\u043e \u0442\u043e\u0432\u0430\u0440\u0430.<\/p>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0441\u0442\u0438, \u0447\u0442\u043e\u0431\u044b \u0437\u0430\u0442\u0440\u0430\u0442\u044b \u0431\u044b\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u043c\u0438, \u043a\u0430\u043a\u043e\u0432\u044b \u044d\u0442\u0438 \u0437\u0430\u0442\u0440\u0430\u0442\u044b \u0438 \u043a\u0430\u043a\u0438\u043c\u0438 \u0431\u044b\u043b\u0438 \u0431\u044b \u0437\u0430\u0442\u0440\u0430\u0442\u044b, \u0435\u0441\u043b\u0438 \u0431\u044b \u043d\u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u044d\u0442\u0438\u0445 \u0442\u043e\u0432\u0430\u0440\u043e\u0432 \u043d\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u043b\u0441\u044f. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 1: \u0423\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0443\u0436\u0435 \u0434\u0430\u0435\u0442 \u043d\u0430\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0430 \u0438\u043c\u0435\u043d\u043d\u043e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6dc6eb92c2776f8026c348e7e5824d09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=40-6x+x^2 .\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"160\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 2: \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438.<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5056826599d14c0ff8aa3ec134a68b0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=40-6x+x^2 \\ \\longrightarrow \\ f'(x)=-6+2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"332\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 3: \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0440\u0435\u0448\u0430\u0435\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-58dcd049349f740f082d583dfd9e364c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ecec21f50b0875af5ebb5c55ef5e2502_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-6+2x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"95\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d47687d0a8cb82ab26be7eadf0d7f3c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x=6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f1ffe509b34b0d560397fbc1859cb64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{6}{2} = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"77\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 4: \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041c\u044b \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u0443\u044e \u0441\u043f\u0440\u0430\u0432\u0430: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-3.webp\" alt=\"\" class=\"wp-image-2485\" width=\"231\" height=\"90\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043e\u0446\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u0438\u043b\u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (\u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443) \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2647164feab3d1bdc3e7cdb14c123294_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(0)=-6+2\\cdot 0=-6\\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"235\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fe3f1add3273a0ba4d0418a3b9788a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(4)=-6+2\\cdot 4=-6+8=2\\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"298\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-3-negatif-positif.webp\" alt=\"\" class=\"wp-image-2486\" width=\"231\" height=\"163\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0443\u043b\u044f, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u043d\u0430 \u044d\u0442\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0435\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043c\u0435\u043d\u044c\u0448\u0435 \u043d\u0443\u043b\u044f, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u044d\u0442\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0420\u043e\u0441\u0442:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbc0e31e2b07080a4f83c2a34053c0f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(3,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0421\u043d\u0438\u0436\u0430\u0442\u044c\u0441\u044f:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a890e45091b2c4c9115051361c0a1a2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f \u043a \u0443\u0432\u0435\u043b\u0438\u0447\u0435\u043d\u0438\u044e \u043f\u0440\u0438 x=3, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=3 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0435 \u0437\u0430\u0442\u0440\u0430\u0442\u044b \u0431\u0443\u0434\u0443\u0442 \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442\u044b \u043f\u0440\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0441\u0442\u0432\u0435 <strong>3000 \u0435\u0434\u0438\u043d\u0438\u0446.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442\u0441\u044f \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c, \u0432 \u0438\u0441\u0445\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a1c84d3c81fd4c7ebbecc922cc2288e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3)=40-6\\cdot 3+3^2=\\bm{31}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"206\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u043c\u0438\u043b\u043b\u0438\u043e\u043d\u044b \u0435\u0432\u0440\u043e.<\/p>\n<p class=\"has-text-align-left\"> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043e\u043d\u0438 \u0441\u043f\u0440\u0430\u0448\u0438\u0432\u0430\u044e\u0442 \u043d\u0430\u0441, \u043a\u0430\u043a\u043e\u0432\u044b \u0431\u044b\u043b\u0438 \u0431\u044b \u0437\u0430\u0442\u0440\u0430\u0442\u044b, \u0435\u0441\u043b\u0438 \u0431\u044b \u043d\u0438\u0447\u0435\u0433\u043e \u043d\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u043b\u043e\u0441\u044c, \u0442\u043e \u0435\u0441\u0442\u044c \u043a\u043e\u0433\u0434\u0430<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa5140cb12e100167e56a99c53750148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f92d7beea0ed3a053927c2d429d3450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7051466b3981f72509f3e5e2aa1d2f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=40-6\\cdot 0+0^2=   \\bm{40}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u043c\u0438\u043b\u043b\u0438\u043e\u043d\u044b \u0435\u0432\u0440\u043e.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 4<\/h3>\n<p> \u041c\u044b \u0445\u043e\u0442\u0438\u043c \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0439 \u0434\u0435\u0440\u0435\u0432\u044f\u043d\u043d\u044b\u0439 \u043a\u0430\u0440\u043a\u0430\u0441, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0438\u0432\u0430\u044e\u0449\u0438\u0439 \u043f\u043b\u043e\u0449\u0430\u0434\u044c 2 \u043c <sup>2<\/sup> . \u041c\u044b \u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e \u0446\u0435\u043d\u0430 \u0434\u0440\u0435\u0432\u0435\u0441\u0438\u043d\u044b \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 7,5 \u0435\u0432\u0440\u043e\/\u043c \u0434\u043b\u044f \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u0442\u043e\u0440\u043e\u043d \u0438 12,5 \u0435\u0432\u0440\u043e\/\u043c \u0434\u043b\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u0442\u043e\u0440\u043e\u043d. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0434\u043e\u043b\u0436\u0435\u043d \u0438\u043c\u0435\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a, \u0447\u0442\u043e\u0431\u044b \u043e\u0431\u0449\u0430\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c \u0440\u0430\u043c\u044b \u0431\u044b\u043b\u0430 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0439 \u0438 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u0430\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c \u0431\u044b\u043b\u0430 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0439. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 1: \u0423\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0414\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430\u0437\u043e\u0432\u0435\u043c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u0442\u043e\u0440\u043e\u043d\u0443 <em>x<\/em> , \u0430 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u0442\u043e\u0440\u043e\u043d\u0443 <em>y<\/em> : <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/rectangle-fonction-optimisation-problemes.webp\" alt=\"\u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\" class=\"wp-image-2490\" width=\"166\" height=\"188\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041f\u043e\u043a\u0443\u043f\u043a\u0430 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0441\u0442\u043e\u0438\u0442 7,5 \u0435\u0432\u0440\u043e, \u0430 \u043f\u043e\u043a\u0443\u043f\u043a\u0430 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u2014 12,5 \u0435\u0432\u0440\u043e. \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u043a\u0430\u0434\u0440\u0430 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u044b \u0434\u0432\u0435 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0438 \u0434\u0432\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c \u043a\u0430\u0434\u0440\u0430 \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8485280ab046816dfbd587b192901fb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(x,y)= 7,5\\cdot 2x+12,5 \\cdot 2y = 15x +25y\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"323\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0443 \u043d\u0430\u0441 \u0443\u0436\u0435 \u0435\u0441\u0442\u044c. \u041d\u043e \u043e\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0434\u0432\u0443\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u0445\u043e\u0442\u044f \u043c\u043e\u0436\u0435\u0442 \u0437\u0430\u0432\u0438\u0441\u0435\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u043e\u0434\u043d\u043e\u0439. \u041e\u0434\u043d\u0430\u043a\u043e \u0432 \u0437\u0430\u044f\u0432\u043b\u0435\u043d\u0438\u0438 \u043d\u0430\u043c \u0441\u043a\u0430\u0437\u0430\u043d\u043e, \u0447\u0442\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438 \u043a\u0430\u0440\u043a\u0430\u0441\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0442\u044c 2 \u043c <sup>2<\/sup> . \u0415\u0449\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-13ea4da7e9b4674fdd1a733e0e3cd26e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x \\cdot y = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"64\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0423\u0434\u0430\u043b\u044f\u0435\u043c \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0443\u044e <em>y<\/em> :<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e00a5c6da8de49964d27f2941dac8a4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =\\cfrac{2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"46\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u043c\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2cb9add65869ac746532ac4bf1537eb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(x,y)= 15x +25y\\ \\xrightarrow{y \\ = \\ \\frac{2}{x} } \\ C(x)= 15x+25\\left(\\cfrac{2}{x} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"396\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e232dbf6025d3b8d6593e4157cd09bff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(x)= 15x+\\cfrac{50}{x} =15x +50x^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 2: \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438.<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ef3647de078c1f760dc37a5d3d6b68e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(x)=15x +50x^{-1} \\ \\longrightarrow \\ C'(x)=15 -50x^{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"359\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 3: \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0440\u0435\u0448\u0430\u0435\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97f234a562c87b78e257fc7953dee7ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8732228827d41a41af6935b1f0bdc0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdaf71028a32e2818a7ec3376338df75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15 -50x^{-2}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"117\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8bf1bee39e8e6e8f54b838f7dc8810d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15 =50x^{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"86\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4f9337813bfb8c7bf0d09f9889514c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15=\\cfrac{50}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"60\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0aea588515cc1c895b2ca5030cd55ffc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{15}{1}=\\cfrac{50}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"61\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0423\u043c\u043d\u043e\u0436\u0438\u043c \u043f\u043e\u043f\u0435\u0440\u0435\u0447\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0440\u0435\u0448\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441 \u0434\u0440\u043e\u0431\u044f\u043c\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99a602636bc09eb630e637ec6454c8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15 \\cdot x^2 = 50 \\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"110\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dcdd7918a1af31e63925cb694da7d6be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2 = \\cfrac{50}{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"61\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e9090b3956470b16769ec2ae441f2d30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2 = 3,33\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-92abf359db44a399822919b1bb62e7cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^2} = \\sqrt{3,33}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"105\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b87ffa5999c0bbea78cc07d6a412460a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = 1,83\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"69\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 4: \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u0443\u044e \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-183.webp\" alt=\"\" class=\"wp-image-2491\" width=\"206\" height=\"80\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043e\u0446\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u0438\u043b\u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (\u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443) \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64f2221e9103ecdcb21609567e990135_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(1)=15 -50\\cdot 1^{-2} = 15-50 = -35 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"347\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad12501e06c6997d1555df684480d38b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2)=15 -50\\cdot 2^{-2} = 15-12,5 = 2,5 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"358\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-183-negatif-positif.webp\" alt=\"\" class=\"wp-image-2493\" width=\"206\" height=\"146\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442, \u0430 \u0435\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0431\u044b\u0432\u0430\u0435\u0442. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0440\u043e\u0441\u0442\u0430 \u0438 \u043f\u0430\u0434\u0435\u043d\u0438\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0420\u043e\u0441\u0442:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d8e4f82a46ac576b10134beda86f0bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,83,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0421\u043d\u0438\u0436\u0430\u0442\u044c\u0441\u044f:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57f0911e594b424ad7908294a15f1b84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,1,83)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f \u043a \u0443\u0432\u0435\u043b\u0438\u0447\u0435\u043d\u0438\u044e \u043f\u0440\u0438 x=1,83, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=1,83 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p class=\"has-text-align-left\"> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, x=1,83 \u2014 \u044d\u0442\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c. \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-325134d449963e4d814cdd19a87bdfd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =\\cfrac{2}{x} \\ \\longrightarrow \\ y =\\cfrac{2}{1,83} = \\bm{1,09}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"223\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0435 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c \u043a\u0430\u0440\u043a\u0430\u0441\u0430, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442:<\/p>\n<p class=\"has-text-align-center\"> \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0442\u043e\u0440\u043e\u043d\u0430<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c8b9148690c3a5b5e441df6c02e23e85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"= x = \\bm{1,83} \\ \\mathbf{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"110\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0442\u043e\u0440\u043e\u043d\u0430<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ad15cb0e6023282190abbb21c5f8a47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"= y = \\bm{1,09} \\ \\mathbf{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c, \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u043c\u0430\u044f \u043f\u0440\u0438 \u044d\u0442\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bef42a21eacaeb4cd25b5e43c15e268b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C= 15\\cdot 1,83+25\\cdot 1,09=\\bm{54,70}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"256\" style=\"vertical-align: -4px;\"><\/p>\n<p> <strong>\u20ac<\/strong><\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 5<\/h3>\n<p> \u0414\u0432\u0435\u0440\u044c \u0441\u043e\u0431\u043e\u0440\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043f\u043e\u043b\u0443\u043a\u0440\u0443\u0433\u043b\u0443\u044e \u0430\u0440\u043a\u0443, \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u0438\u0432\u0430\u0435\u043c\u0443\u044e \u0434\u0432\u0443\u043c\u044f \u043a\u043e\u043b\u043e\u043d\u043d\u0430\u043c\u0438, \u043a\u0430\u043a \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u0440\u0438\u0441\u0443\u043d\u043a\u0435: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/problemes-d-optimisation-de-la-geometrie.webp\" alt=\"\u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438\" class=\"wp-image-2500\" width=\"182\" height=\"268\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u0415\u0441\u043b\u0438 \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0434\u0432\u0435\u0440\u0438 20 \u043c, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u044b<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0447\u0442\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0432\u0430\u0435\u0442 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438 \u0432\u0441\u0435\u0439 \u0434\u0432\u0435\u0440\u0438. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 1: \u0423\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041f\u043b\u043e\u0449\u0430\u0434\u044c \u043a\u0440\u0443\u0433\u0430 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1ab0b6b8d454bae5631e7a82caed58d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi r^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0417\u043d\u0430\u0447\u0438\u0442 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0432\u0441\u0435\u0439 \u0434\u0432\u0435\u0440\u0438 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u043d\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u043f\u043b\u044e\u0441 \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-95c1f9b6152c4cbc623aeb8a0a5757b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x\\cdot y + \\cfrac{1}{2} \\left[ \\pi r ^2 \\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-baa2e14b061cf14a657782db8fe91b92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x y + \\cfrac{1}{2} \\left[ \\pi \\left(\\cfrac{x}{2}\\right)^2 \\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"212\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9196d8284edebe6450d49aa5a0b6a3e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x y + \\cfrac{1}{2} \\left[ \\pi \\cdot \\cfrac{x^2}{4} \\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"193\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b25e1d2c661585be998d1596d6650c01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x y +\\cfrac{1}{2} \\left[  \\cfrac{\\pi \\cdot x^2}{4} \\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"193\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64a0c7fa480320a1b564fec5f9ff8265_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= xy +\\cfrac{\\pi x^2}{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"150\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0443 \u043d\u0430\u0441 \u0443\u0436\u0435 \u0435\u0441\u0442\u044c. \u041d\u043e \u043e\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0434\u0432\u0443\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u0445\u043e\u0442\u044f \u043c\u043e\u0436\u0435\u0442 \u0437\u0430\u0432\u0438\u0441\u0435\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u043e\u0434\u043d\u043e\u0439.<\/p>\n<p class=\"has-text-align-left\"> \u041e\u0434\u043d\u0430\u043a\u043e \u0432 \u0440\u0435\u043b\u0438\u0437\u0435 \u0441\u043a\u0430\u0437\u0430\u043d\u043e, \u0447\u0442\u043e \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0432\u0441\u0435\u0445 \u0432\u043e\u0440\u043e\u0442 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 20 \u043c\u0435\u0442\u0440\u043e\u0432. \u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u043a\u0440\u0443\u0433\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e815d233e188a7121eef89639e48fe75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\pi r.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0432\u0441\u0435\u0439 \u0434\u0432\u0435\u0440\u0438 \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7709d0c72bf84a17ac83bc46f5cce002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P= x +2y +\\cfrac{1}{2} \\left[ 2 \\pi \\left( \\cfrac{x}{2}\\right) \\right] = x+2y + \\cfrac{2 \\pi x }{2 \\cdot 2} = x+2y + \\cfrac{ \\pi x }{2 }\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"452\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c 20 \u043c. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u043b\u0438 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u044b\u043c 20, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a70e6a4387a816f153e8597195143f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-282aa8aebdd04ba4989ba7466fdd694d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+2y + \\cfrac{ \\pi x }{2 } = 20\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"136\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0423\u043c\u043d\u043e\u0436\u0430\u0435\u043c \u0432\u0441\u0435 \u0447\u043b\u0435\u043d\u044b \u043d\u0430 2, \u0447\u0442\u043e\u0431\u044b \u0438\u0441\u043a\u043b\u044e\u0447\u0438\u0442\u044c \u0434\u0440\u043e\u0431\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a185cfda7fb65f370636fa469b0de2c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot x+2\\cdot 2y + 2 \\cdot \\cfrac{ \\pi x }{2 } = 2 \\cdot 20\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"223\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d67cd2fbdde0f884603e75bf270cb52c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+4y +  \\pi x = 40\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"143\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041c\u044b \u043e\u0447\u0438\u0449\u0430\u0435\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a70e6a4387a816f153e8597195143f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-740ff13a6824a3ee18cb1de0cbf52660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4y  = 40-2x- \\pi x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"143\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db16e16a94223af02d63ea70eae3db7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y   = \\cfrac{40-2x- \\pi x}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"136\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u043c\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16c3b1d1a3ac443d4640ae2b72c164e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x y +\\cfrac{\\pi x^2}{8}\\ \\xrightarrow{y \\ = \\ \\frac{40-2x- \\pi x}{4} }\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"262\" style=\"vertical-align: -12px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f463f9095e8028624678c06a08696a96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x)= x \\cdot \\cfrac{40-2x- \\pi x}{4}+\\cfrac{\\pi x^2}{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"239\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-095586f92b592c3c9c50750f8a6eb7d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x)= \\cfrac{40x-2x^2-\\pi x^2}{4}+\\cfrac{\\pi x^2}{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"242\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 2: \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438.<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42ce3330af662099ad431ee1187d26f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x)=\\cfrac{(40-4x-2\\pi x)\\cdot 4 +(40x-2x^2- \\pi x^2)\\cdot 0 }{4^2} +\\cfrac{2\\pi x \\cdot 8 + \\pi x^2 \\cdot 0}{8^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"544\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a75cddf1efd4f17b6a3211093f2e0b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x)=\\cfrac{160-16x-8\\pi x }{16} +\\cfrac{16\\pi x}{64}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"257\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 3: \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0440\u0435\u0448\u0430\u0435\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8f5a921f7e1978b553d11a76e0962c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-424f3d5d91120e872bebd055792d71a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89a04d2a2a532f36f15042d2d2c79d41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{160-16x-8\\pi x }{16} +\\cfrac{16\\pi x}{64} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"222\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u042d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441 \u0434\u0440\u043e\u0431\u044f\u043c\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0443\u043c\u043d\u043e\u0436\u0430\u0435\u043c \u043a\u0430\u0436\u0434\u043e\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 \u043d\u0430 1\u0441\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435\u0439, \u0447\u0442\u043e\u0431\u044b \u0438\u0441\u043a\u043b\u044e\u0447\u0438\u0442\u044c \u0434\u0440\u043e\u0431\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-87d60f06d42276c79b3a4f33b00fdb7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"64 \\cdot \\cfrac{160-16x-8\\pi x }{16} +64 \\cdot \\cfrac{16\\pi x}{64} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"285\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2a7b3bbdad1ea1bf9f12861b1dbdf0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot ( 160-16x-8\\pi x) +1\\cdot 16\\pi x= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61a4622d4b65310580e066941ae13fac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"640-64x -32 \\pi x +16\\pi x= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"229\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-94c6efd66ea5f2f1c68ab09d59fb5432_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-64x -32 \\pi x +16\\pi x= -640\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"226\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bdaf73c6d74c3d4f605b5aea3cdeb1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-64x -16 \\pi x = -640\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4bfe710d37882f664daed4de23f2eb7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-64 -16 \\pi) x = -640\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b551560fd86665e639dbc88aeb88a2bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-640}{-64 -16 \\pi}  = 5,6\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"167\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 4: \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0414\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u0443\u044e \u0441\u043f\u0440\u0430\u0432\u0430: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-56.webp\" alt=\"\" class=\"wp-image-2501\" width=\"214\" height=\"83\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043e\u0446\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u0438\u043b\u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (\u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443) \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8b0c6b03e591be56505c8853595dd0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(0)=\\cfrac{160-16\\cdot 0-8\\pi \\cdot 0 }{16} +\\cfrac{16\\pi \\cdot 0}{64} = 10 +0 = 10 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"456\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91c7e9012e4937dad79ec792910df916_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(6)=\\cfrac{160-16\\cdot 6-8\\pi \\cdot 6 }{16} +\\cfrac{16\\pi \\cdot 6}{64} = -5,42 +4,71 = -0,71 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"543\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-56-positif-negatif.webp\" alt=\"\" class=\"wp-image-2503\" width=\"218\" height=\"155\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442, \u0430 \u0435\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0431\u044b\u0432\u0430\u0435\u0442. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0440\u043e\u0441\u0442\u0430 \u0438 \u043f\u0430\u0434\u0435\u043d\u0438\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0420\u043e\u0441\u0442:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-375f15fd5182721ee68f606765b66e89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty , 5,6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0421\u043d\u0438\u0436\u0430\u0442\u044c\u0441\u044f:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce3629c3ea3fa84fd3413a15913976f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(5,6,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u043a \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044e \u043f\u0440\u0438 x=5,6, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=5,6 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p class=\"has-text-align-left\"> \u0415\u0449\u0435,<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0d40793b19725cb50b88536bdaf3239_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5,6\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"60\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u044d\u0442\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u044c. \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a70e6a4387a816f153e8597195143f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-af3ff0bf06cb82b6661c9ead44cabaa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = \\cfrac{40-2\\cdot 5,6- \\pi \\cdot 5,6}{4} = 2,80\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"251\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u044c, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25cd4efdc51c2a6fb453056df61536fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x = 5,60} \\ \\mathbf{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b69c85499698e995f01f60b2b78ef20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y = 2,80} \\ \\mathbf{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 6<\/h3>\n<p> \u041c\u044b \u0445\u043e\u0442\u0438\u043c \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0440\u0435\u0437\u0435\u0440\u0432\u0443\u0430\u0440 \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u043e\u0440\u043c\u044b \u043f\u043b\u043e\u0449\u0430\u0434\u044c\u044e 54 \u0441\u043c <sup>2<\/sup> . \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0440\u0430\u0434\u0438\u0443\u0441 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u0438 \u0432\u044b\u0441\u043e\u0442\u0443 \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0430 \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043e\u0431\u044a\u0435\u043c \u0431\u044b\u043b \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u043c. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 1: \u0423\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041e\u0431\u044a\u0435\u043c \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0430 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbe33001d54c8245539894746beb9eac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V= A_{base}\\cdot h\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"101\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043b\u043e\u0449\u0430\u0434\u044c \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u2014 \u043a\u0440\u0443\u0433, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc935e01b9c94505406438dea94cf121_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_{\\text{base}}=\\pi r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -3px;\"><\/p>\n<p> . \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043e\u0431\u044a\u0435\u043c\u0430 \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0430 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df6ffff5ee54af4f7b10424871d1af92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V= \\pi r^2 \\cdot h\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"88\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0443 \u043d\u0430\u0441 \u0443\u0436\u0435 \u0435\u0441\u0442\u044c. \u041d\u043e \u044d\u0442\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0434\u0432\u0443\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 (<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> ), \u0445\u043e\u0442\u044f \u044d\u0442\u043e \u043c\u043e\u0436\u0435\u0442 \u0437\u0430\u0432\u0438\u0441\u0435\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u043e\u0434\u043d\u043e\u0433\u043e. \u041e\u0434\u043d\u0430\u043a\u043e \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u0435 \u0433\u043e\u0432\u043e\u0440\u0438\u0442 \u043d\u0430\u043c, \u0447\u0442\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c 54 \u0441\u043c <sup>2<\/sup> , \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u044d\u0442\u0438\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u0435\u043c, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f0bf134a8aafe0dfaa4d711f78b8b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0441\u043b\u043e\u0436\u0438\u0442\u044c \u0435\u0433\u043e \u0431\u043e\u043a\u043e\u0432\u0443\u044e \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0441 \u043f\u043b\u043e\u0449\u0430\u0434\u044f\u043c\u0438 \u0434\u0432\u0443\u0445 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0439: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/problemes-optimisation-des-fonctions-verins.webp\" alt=\"\u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0430.png\" class=\"wp-image-2507\" width=\"557\" height=\"271\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-edd9578a95d32143e6eaf0830db3854b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_{cilindro} = A_{lateral}+2A_{base} = 2\\pi r h + 2\\pi r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"330\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043b\u043e\u0449\u0430\u0434\u044c \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c 54 \u0441\u043c <sup>2<\/sup> , \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u043e\u043b\u043e\u0436\u0438\u043c \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u044b\u043c 54, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6868abdfd034048aa59644d2ac62353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ef4f7f8554876495f8907d4f71e1152_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_{cilindro} =2\\pi r h + 2\\pi r^2 = 54\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"223\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041c\u044b \u043e\u0447\u0438\u0449\u0430\u0435\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6868abdfd034048aa59644d2ac62353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd73c08d458b0ab2061031782d125ab9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\pi r h = 54 - 2\\pi r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"136\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-abf53b37d2a3ae4784079bfd67d3007f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h = \\cfrac{54 - 2\\pi r^2}{2\\pi r}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"112\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u043c\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2c47f99ce14b444ed73661b2b568e8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V=  \\pi r^2 \\cdot h \\xrightarrow{h \\ = \\ \\frac{54 - 2\\pi r^2}{2\\pi r} } V = \\pi r^2 \\cdot \\cfrac{54 - 2\\pi r^2}{2\\pi r}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"346\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-81d564fcd7cdf880066ed3eb6eb9a18a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V = \\cancel{\\pi}  r^{\\cancel{2}} \\cdot \\cfrac{54 - 2\\pi r^2}{2 \\cancel{\\pi} \\cancel{r}} =r \\cdot \\cfrac{54 - 2\\pi r^2}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"278\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f95e7e1fc6088ba84a7b3885fe929d58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V(r) = r \\cdot (27 - \\pi r^2)= 27r - \\pi r^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"259\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 2: \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438.<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-58e3403f2812564067058ece1bcd83ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V(r)=27r - \\pi r^3\\ \\longrightarrow \\ V'(r)= 27-3 \\pi r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"324\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 3: \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0440\u0435\u0448\u0430\u0435\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e868c9ed52907fbe13197b00c29b7d21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V'(r)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3de17aa96e46530402559cf14e8db4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V'(r)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10638a98b4a67b085c0854f95c86a65b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27-3 \\pi r^2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e31d335383816f692cd02cb2ca8f55b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3 \\pi r^2=-27\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"104\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ff57ef2a3aa07b3c9f9f76a9cb00f484_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r^2=\\cfrac{-27}{-3\\pi }\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"82\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d9e55eb22dc67a402b53bbb9ca17298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r^2=2,86\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8c7c4c4acf5b028e2dbba11dfc83d20b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{r^2}=\\sqrt{2,86}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"103\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01af3fa2bc910bd2da923aa2c83e1d7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r=1,69\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"67\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>\u0428\u0430\u0433 4: \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0414\u043b\u044f \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u0443\u044e \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u043d\u0430 \u0447\u0438\u0441\u043b\u043e\u0432\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-169.webp\" alt=\"\" class=\"wp-image-2508\" width=\"232\" height=\"90\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043e\u0446\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u0438\u043b\u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (\u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0442\u043e\u0447\u043a\u0443) \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d2aa45b6cfc986ec1e33cdd5e9266e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V'(0)= 27-3 \\pi\\cdot 0^2 = 27-0 = +27 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"333\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c599118454ccdcc0e318f01ac61b84d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V'(2)= 27-3 \\pi \\cdot 2^2 = 27-37,70 = -10,70 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"393\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-169-positif-negatif.webp\" alt=\"\" class=\"wp-image-2509\" width=\"249\" height=\"176\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442, \u0430 \u0435\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0431\u044b\u0432\u0430\u0435\u0442. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0440\u043e\u0441\u0442\u0430 \u0438 \u043f\u0430\u0434\u0435\u043d\u0438\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0420\u043e\u0441\u0442:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5e2776182fc7c0a5138adfee1aafaaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,1,69)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0421\u043d\u0438\u0436\u0430\u0442\u044c\u0441\u044f:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f4ac44f6269498e03069a77e1989c8be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,69,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u043a \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044e \u043f\u0440\u0438 r=1,69, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>r=1,69 \u0441\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p class=\"has-text-align-left\"> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, r=1,69 \u2014 \u044d\u0442\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0440\u0430\u0434\u0438\u0443\u0441\u0430, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u043c. \u0422\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0432\u044b\u0441\u043e\u0442\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-381f3c5eb279572f486e28e68f0c5af2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h = \\cfrac{54 - 2\\pi \\cdot 1,69^2}{2\\pi \\cdot1,69} = \\cfrac{54 - 17,94}{10,62} = 3,39\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"316\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u0433\u0440\u043e\u043c\u043a\u043e\u0441\u0442\u044c:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0420\u0430\u0434\u0438\u043e<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c99f9d93c8a300be7afef76dfb71379_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{= r = 1,69} \\ \\mathbf{cm}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"117\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0412\u044b\u0441\u043e\u0442\u0430<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ee2564c5e4b2a4e4409c392e5d01627_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{= h = 3,39} \\ \\mathbf{cm}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"119\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u044d\u0442\u0430\u043f\u043d\u043e \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438, \u0440\u0435\u0448\u0430\u044e\u0449\u0438\u043c\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438? \u0417\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043d\u0430\u0439\u0442\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u043c\u043e\u0436\u0435\u0442 \u0432\u043a\u043b\u044e\u0447\u0430\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0449\u0435\u0439 \u043f\u0440\u0438\u0431\u044b\u043b\u044c \u043a\u043e\u043c\u043f\u0430\u043d\u0438\u0438. \u041a\u0430\u043a \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u043f\u043e \u0443\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0431\u043b\u0435\u043c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/\"> <span class=\"screen-reader-text\">\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[17],"tags":[],"class_list":["post-45","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 -<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ru\/\u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b-\u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 -\" \/>\n<meta property=\"og:description\" content=\"\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u044d\u0442\u0430\u043f\u043d\u043e \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438, \u0440\u0435\u0448\u0430\u044e\u0449\u0438\u043c\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438? \u0417\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043d\u0430\u0439\u0442\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u043c\u043e\u0436\u0435\u0442 \u0432\u043a\u043b\u044e\u0447\u0430\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0449\u0435\u0439 \u043f\u0440\u0438\u0431\u044b\u043b\u044c \u043a\u043e\u043c\u043f\u0430\u043d\u0438\u0438. \u041a\u0430\u043a \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u043f\u043e \u0443\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0431\u043b\u0435\u043c &hellip; \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ru\/\u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b-\u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T10:57:01+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-optimisation-probleme.webp\" \/>\n<meta name=\"author\" content=\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e \u0430\u0432\u0442\u043e\u0440\u043e\u043c\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/\"},\"author\":{\"name\":\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\",\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/person\/69fe5e2ffd89c6227f6a42153bb3655b\"},\"headline\":\"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438\",\"datePublished\":\"2023-09-17T10:57:01+00:00\",\"dateModified\":\"2023-09-17T10:57:01+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/\"},\"wordCount\":1980,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/ru\/#organization\"},\"articleSection\":[\"\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\"],\"inLanguage\":\"ru-RU\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/\",\"url\":\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/\",\"name\":\"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 -\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/ru\/#website\"},\"datePublished\":\"2023-09-17T10:57:01+00:00\",\"dateModified\":\"2023-09-17T10:57:01+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/#breadcrumb\"},\"inLanguage\":\"ru-RU\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/ru\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/ru\/#website\",\"url\":\"https:\/\/mathority.org\/ru\/\",\"name\":\"Mathority\",\"description\":\"\u0413\u0434\u0435 \u043b\u044e\u0431\u043e\u043f\u044b\u0442\u0441\u0442\u0432\u043e \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u0442\u0441\u044f \u0441 \u0440\u0430\u0441\u0447\u0435\u0442\u043e\u043c!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/ru\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/ru\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"ru-RU\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/ru\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/ru\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ru-RU\",\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/ru\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/ru\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/person\/69fe5e2ffd89c6227f6a42153bb3655b\",\"name\":\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ru-RU\",\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\"},\"sameAs\":[\"http:\/\/mathority.org\/ru\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 -","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/ru\/\u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b-\u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438\/","og_locale":"ru_RU","og_type":"article","og_title":"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 -","og_description":"\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u044d\u0442\u0430\u043f\u043d\u043e \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438, \u0440\u0435\u0448\u0430\u044e\u0449\u0438\u043c\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438? \u0417\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043d\u0430\u0439\u0442\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u043c\u043e\u0436\u0435\u0442 \u0432\u043a\u043b\u044e\u0447\u0430\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0449\u0435\u0439 \u043f\u0440\u0438\u0431\u044b\u043b\u044c \u043a\u043e\u043c\u043f\u0430\u043d\u0438\u0438. \u041a\u0430\u043a \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u043f\u043e \u0443\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0431\u043b\u0435\u043c &hellip; \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;","og_url":"https:\/\/mathority.org\/ru\/\u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b-\u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438\/","article_published_time":"2023-09-17T10:57:01+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-optimisation-probleme.webp"}],"author":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430","twitter_card":"summary_large_image","twitter_misc":{"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e \u0430\u0432\u0442\u043e\u0440\u043e\u043c":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/"},"author":{"name":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430","@id":"https:\/\/mathority.org\/ru\/#\/schema\/person\/69fe5e2ffd89c6227f6a42153bb3655b"},"headline":"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438","datePublished":"2023-09-17T10:57:01+00:00","dateModified":"2023-09-17T10:57:01+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/"},"wordCount":1980,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/ru\/#organization"},"articleSection":["\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438"],"inLanguage":"ru-RU","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/","url":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/","name":"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 -","isPartOf":{"@id":"https:\/\/mathority.org\/ru\/#website"},"datePublished":"2023-09-17T10:57:01+00:00","dateModified":"2023-09-17T10:57:01+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/#breadcrumb"},"inLanguage":"ru-RU","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0%d1%86%d0%b8%d0%b8\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/ru\/"},{"@type":"ListItem","position":2,"name":"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/ru\/#website","url":"https:\/\/mathority.org\/ru\/","name":"Mathority","description":"\u0413\u0434\u0435 \u043b\u044e\u0431\u043e\u043f\u044b\u0442\u0441\u0442\u0432\u043e \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u0442\u0441\u044f \u0441 \u0440\u0430\u0441\u0447\u0435\u0442\u043e\u043c!","publisher":{"@id":"https:\/\/mathority.org\/ru\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/ru\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"ru-RU"},{"@type":"Organization","@id":"https:\/\/mathority.org\/ru\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/ru\/","logo":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/mathority.org\/ru\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/ru\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/ru\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/ru\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/ru\/#\/schema\/person\/69fe5e2ffd89c6227f6a42153bb3655b","name":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430","image":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/mathority.org\/ru\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430"},"sameAs":["http:\/\/mathority.org\/ru"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/posts\/45","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/comments?post=45"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/posts\/45\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/media?parent=45"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/categories?post=45"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/tags?post=45"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}