{"id":47,"date":"2023-09-17T10:56:06","date_gmt":"2023-09-17T10:56:06","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%b2%d0%be%d0%b3%d0%bd%d1%83%d1%82%d0%be%d1%81%d1%82%d0%b8-%d0%b8-%d0%b2%d1%8b%d0%bf%d1%83%d0%ba%d0%bb%d0%be%d1%81%d1%82%d0%b8-%d0%ba%d1%80%d0%b8%d0%b2\/"},"modified":"2023-09-17T10:56:06","modified_gmt":"2023-09-17T10:56:06","slug":"%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%b2%d0%be%d0%b3%d0%bd%d1%83%d1%82%d0%be%d1%81%d1%82%d0%b8-%d0%b8-%d0%b2%d1%8b%d0%bf%d1%83%d0%ba%d0%bb%d0%be%d1%81%d1%82%d0%b8-%d0%ba%d1%80%d0%b8%d0%b2","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%b2%d0%be%d0%b3%d0%bd%d1%83%d1%82%d0%be%d1%81%d1%82%d0%b8-%d0%b8-%d0%b2%d1%8b%d0%bf%d1%83%d0%ba%d0%bb%d0%be%d1%81%d1%82%d0%b8-%d0%ba%d1%80%d0%b8%d0%b2\/","title":{"rendered":"\u0412\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 (\u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0430)"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\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 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u043d\u0430 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-concavidad-y-la-convexidad-de-una-funcion\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0412\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong> <strong>\u0412\u043e\u0433\u043d\u0443\u0442\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/strong> \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0433\u0440\u0430\u0444\u0438\u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0438\u043c\u0435\u0435\u0442 \u0444\u043e\u0440\u043c\u0443 \u0433\u043e\u0440\u044b, \u0430 <strong>\u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/strong> \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0433\u0440\u0430\u0444\u0438\u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0438\u043c\u0435\u0435\u0442 \u0444\u043e\u0440\u043c\u0443 \u0434\u043e\u043b\u0438\u043d\u044b.<\/p>\n<p> \u0412 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0430\u0431\u0437\u0430\u0446\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u044b\u043b\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u044b \u043d\u0435\u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u0434\u043b\u044f \u043f\u0440\u043e\u0441\u0442\u043e\u0442\u044b \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f, \u043d\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<ul>\n<li> <strong>\u0412\u043e\u0433\u043d\u0443\u0442\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f:<\/strong> \u043a\u043e\u0433\u0434\u0430 \u043e\u0442\u0440\u0435\u0437\u043e\u043a, \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u044e\u0449\u0438\u0439 \u043b\u044e\u0431\u044b\u0435 \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043d\u0438\u0436\u0435 \u043a\u0440\u0438\u0432\u043e\u0439.<\/li>\n<li> <strong>\u0412\u044b\u043f\u0443\u043a\u043b\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f:<\/strong> \u043a\u043e\u0433\u0434\u0430 \u043e\u0442\u0440\u0435\u0437\u043e\u043a, \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u044e\u0449\u0438\u0439 \u043b\u044e\u0431\u044b\u0435 \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043d\u0430\u0434 \u043a\u0440\u0438\u0432\u043e\u0439. <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-9\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\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\/fonction-concave.webp\" alt=\"\u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f\" class=\"wp-image-2556\" width=\"292\" height=\"300\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\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\/fonction-convexe.webp\" alt=\"\u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f\" class=\"wp-image-2557\" width=\"288\" height=\"300\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p> \u0412 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u043c \u0441\u0447\u0435\u0442\u0435, \u0440\u0430\u0437\u043d\u0438\u0446\u0430 \u043c\u0435\u0436\u0434\u0443 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0437\u0430\u043a\u043b\u044e\u0447\u0430\u0435\u0442\u0441\u044f \u0432 \u0444\u043e\u0440\u043c\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043e\u0442\u043b\u0438\u0447\u0438\u0442\u044c \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u043e\u0442 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u043f\u043e \u0433\u0440\u0430\u0444\u0438\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u041e\u0434\u043d\u0430\u043a\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u0432\u043e \u0432\u0441\u0435\u0439 \u0441\u0432\u043e\u0435\u0439 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043d\u043e \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0432 \u043e\u0434\u043d\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u0432 \u0434\u0440\u0443\u0433\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435.<\/p>\n<p class=\"has-background\" style=\"background-color:#fffde7\"> <strong>\u041f\u0440\u0438\u043c\u0435\u0447\u0430\u043d\u0438\u0435.<\/strong> \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0441\u043e\u043e\u0431\u0449\u0435\u0441\u0442\u0432\u043e \u0434\u043e \u0441\u0438\u0445 \u043f\u043e\u0440 \u043d\u0435 \u0434\u043e \u043a\u043e\u043d\u0446\u0430 \u0441 \u044d\u0442\u0438\u043c \u0441\u043e\u0433\u043b\u0430\u0441\u043d\u044b \u0438 \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u043e\u0440\u0430 \u0433\u043e\u0432\u043e\u0440\u044f\u0442 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435: \u043e\u043d\u0438 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0438\u043c\u0435\u044e\u0449\u0443\u044e \u0444\u043e\u0440\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-f5ebc563dbe58138d1de6b7fe99e8d31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\cup}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0438\u043c\u0435\u044e\u0449\u0430\u044f \u0432\u0438\u0434<strong> <\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dccbfcebef91876585ebd365457c3d24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\cap}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>. \u0412 \u043b\u044e\u0431\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432\u0430\u0436\u043d\u043e \u0437\u043d\u0430\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u0437\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043a\u0430\u043a \u0431\u044b \u043e\u043d\u0430 \u043d\u0438 \u043d\u0430\u0437\u044b\u0432\u0430\u043b\u0430\u0441\u044c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-estudiar-la-curvatura-de-una-funcion\"><\/span> \u041a\u0430\u043a \u0438\u0437\u0443\u0447\u0438\u0442\u044c \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0418\u0437\u0443\u0447\u0435\u043d\u0438\u0435 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u0442 \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u0438 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0442\u043e \u0435\u0441\u0442\u044c \u0437\u043d\u0430\u043d\u0438\u0435 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u043e\u0432, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0433\u043d\u0443\u0442\u0430, \u0438 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u043e\u0432, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u044b\u043f\u0443\u043a\u043b\u0430.<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0434\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f: <\/p>\n<div style=\"background-color:#FFF3E0; padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 10px; border-radius:30px;\">\n<ol style=\"color:#64B5F6; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u041d\u0430\u0439\u0434\u0438\u0442\u0435 <strong>\u0442\u043e\u0447\u043a\u0438, \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0438\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043f\u0435\u0440\u0432\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0438 <strong>\u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u041d\u0430\u0439\u0434\u0438\u0442\u0435 <strong>\u043a\u043e\u0440\u043d\u0438 \u0432\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439<\/strong> , \u0442\u043e \u0435\u0441\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0442\u043e\u0447\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u043e\u043a\u0440\u0430\u0449\u0430\u044e\u0442 \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e, \u0440\u0435\u0448\u0438\u0432\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> .<\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u0421\u0434\u0435\u043b\u0430\u0439\u0442\u0435 <strong>\u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b<\/strong> \u043c\u0435\u0436\u0434\u0443 \u043a\u043e\u0440\u043d\u044f\u043c\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0438 \u0442\u043e\u0447\u043a\u0430\u043c\u0438, \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0438\u043c\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0432\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0430.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, <strong>\u0437\u043d\u0430\u043a \u0432\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439<\/strong> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0430 \u044d\u0442\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435:<\/span>\n<ul style=\"color:#64B5F6; font-weight: bold; margin-top:8px; margin-left:8%\">\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f <strong>\u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f<\/strong> \u043d\u0430 \u044d\u0442\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435.<\/span><\/li>\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430 \u044d\u0442\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 <strong>\u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f<\/strong> .<\/span> <\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-curvatura-de-una-funcion\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0414\u0430\u043b\u0435\u0435 \u043c\u044b \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c \u0440\u0435\u0448\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u044e\u0442\u0441\u044f \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u0438 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<ul>\n<li> \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d76dfe92202a4fa44057a7f4576c97a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-3x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u0435\u0440\u0432\u043e\u0435, \u0447\u0442\u043e \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c, \u044d\u0442\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b:<\/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-4f565027fd5d2a4381e3a23d183c9f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u044f\u0441\u043d\u0438\u0442\u044c, \u0432 \u043a\u0430\u043a\u0438\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u0443\u043b\u044c.<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043f\u0435\u0440\u0432\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \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-5e356b083f137690f09e2af3c62b8b07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-3x \\ \\longrightarrow \\ f'(x)= 3x^2-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"287\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0417\u0430\u0442\u0435\u043c \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \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-016a210c39feb9d6df8caddacdbac681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2-3 \\ \\longrightarrow \\ f''(x)= 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"256\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u044f\u0435\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043a 0 \u0438 \u0440\u0435\u0448\u0438\u043c \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-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(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-7878c5d5f08c25729d37b94ea643bdf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x=0\" 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-108341259f39e597d1e8c926a80dbae6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{0}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"45\" 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-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\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-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p> , \u043c\u044b \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u0441\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0435 \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439. \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u043d\u0435 \u043d\u0430\u0448\u043b\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u043f\u0440\u0438 \u0440\u0430\u0441\u0447\u0435\u0442\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u0442\u043e\u0447\u043a\u0443, \u0441\u043e\u043a\u0440\u0430\u0449\u0430\u044e\u0449\u0443\u044e \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/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-0.webp\" alt=\"\" class=\"wp-image-2426\" width=\"201\" height=\"77\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0437\u043d\u0430\u043a \u0432\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0432 \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, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439. \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\u0438\u0435 \u0442\u043e\u0447\u043a\u0438) \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u0432\u0442\u043e\u0440\u0430\u044f \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-86d5e98dcde33659284eaafb55050852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=6x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" 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-ab7d8a0d32ae8b29c211f51359c61a4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-1) = 6\\cdot (-1)=-6 \\  \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"236\" 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-084869779374d781df1af76f0aa784ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(1) = 6\\cdot 1=+6 \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-0-concave-convexe.webp\" alt=\"\" class=\"wp-image-2561\" width=\"201\" height=\"134\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u0438 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0415\u0441\u043b\u0438 \u0432\u0442\u043e\u0440\u0430\u044f \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\u044b\u043f\u0443\u043a\u043b\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-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> , \u0438 \u0435\u0441\u043b\u0438 \u0432\u0442\u043e\u0440\u0430\u044f \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 \u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> . \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u0438 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u044b:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0412\u044b\u043f\u0443\u043a\u043b\u044b\u0439<\/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-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91ffae1f3397d9d66e3159e131554abb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,+\\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>\u0412\u043e\u0433\u043d\u0443\u0442\u044b\u0439<\/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-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong> <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bec51dbadb80b73308bcb5a625cd152f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-concavidad-y-convexidad-de-una-funcion\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u0438 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\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-9cd1ae6bdb4d8dbd44ef2561f6e022fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^3-3x^2-2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u043e\u043c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b:<\/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-4f565027fd5d2a4381e3a23d183c9f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u0440\u043e\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c \u0435\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-0a14436352ca08e03441a24b9e881093_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-3x^2-2x \\ \\longrightarrow \\  f'(x)= 3x^2-6x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"375\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0417\u0430\u0442\u0435\u043c \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \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-8ec8542448a8f4aa326a2d70f5f5efb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)= 3x^2-6x-2 \\ \\longrightarrow \\ f''(x)= 6x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"327\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u044f\u0435\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043a 0 \u0438 \u0440\u0435\u0448\u0438\u043c \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-f618f4961c18c45be60fc496ad4896e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(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-5c644c35f109a535e50e1bda440f12db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x-6= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" 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-7b7a2a9a8deaab9c4eb4761838f99407_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x= 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-8ddd3a5381ed7b33d4e9dfbc270c1da3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= \\cfrac{6}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"45\" 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-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u0440\u0435\u0448\u0438\u043b\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-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p> , \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0432\u0441\u0435 \u043e\u0441\u043e\u0431\u044b\u0435 \u0442\u043e\u0447\u043a\u0438, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0435 \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-1.webp\" alt=\"\" class=\"wp-image-2564\" width=\"213\" height=\"83\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0432\u043e\u0437\u044c\u043c\u0435\u043c \u0442\u043e\u0447\u043a\u0443, \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0443\u044e \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0443, \u0438 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u0432\u0442\u043e\u0440\u0430\u044f \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-4e4f2f534e4134661dfda2b6b8125ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(0)= 6\\cdot 0-6 = -6 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"225\" 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-59d344f0c0b93695edf55652112bf6e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(2)= 6\\cdot 2-6 = 12-6=+6 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"297\" 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-1-concave-convexe.webp\" alt=\"\" class=\"wp-image-2565\" width=\"224\" height=\"150\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041a\u043e\u0433\u0434\u0430 \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0443\u043b\u044f, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u044b\u043f\u0443\u043a\u043b\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-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> , \u043d\u043e \u043a\u043e\u0433\u0434\u0430 \u0432\u0442\u043e\u0440\u0430\u044f \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 \u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> . \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u0438 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0440\u0430\u0432\u043d\u044b:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0412\u044b\u043f\u0443\u043a\u043b\u044b\u0439<\/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-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-87d6843b66a0ebea6c769017a30a8d75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,+\\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>\u0412\u043e\u0433\u043d\u0443\u0442\u044b\u0439<\/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-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong> <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36b85798b30f125fea3702a0671c77ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" 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\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\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-3ac9ccc5e8540cca38f599ed36507792_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{x^3}{x^2-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"109\" style=\"vertical-align: -12px;\"><\/p>\n<\/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\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043c\u044b \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043a \u043d\u0443\u043b\u044e, \u0447\u0442\u043e\u0431\u044b \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a\u0438\u0435 \u0447\u0438\u0441\u043b\u0430 \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \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-a34dfe78d673534873a2013c16e1b353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-4= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" 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-c269e23a1070b3e5556abece040af75a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" 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-c4c32359b264b28ac80f2606c09d5a2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^2}=\\sqrt{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" 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-c06a55e3acdd1e283973786926b27716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u042d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043a\u043e\u0433\u0434\u0430 x \u0440\u0430\u0432\u0435\u043d -2 \u0438\u043b\u0438 +2, \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d 0. \u0418, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0431\u0443\u0434\u0435\u0442 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0432\u0441\u0435\u0445 \u0447\u0438\u0441\u0435\u043b, \u043a\u0440\u043e\u043c\u0435 x=-2 \u0438 x=+2.<\/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-e666f828709575f965b5120fbdda085e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}-\\{-2, +2 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u043e-\u0432\u0442\u043e\u0440\u044b\u0445, \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043f\u0435\u0440\u0432\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \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-1397d0e8e73bd7b1d851411dee28daed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3}{x^2-4}  \\ \\longrightarrow \\ f'(x)= \\cfrac{3x^2 \\cdot (x^2-4) - x^3 \\cdot 2x }{\\left(x^2-4\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"396\" style=\"vertical-align: -20px;\"><\/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-495f08a881718b2734ef1db17b5f39ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)= \\cfrac{3x^4-12x^2-2x^4}{\\left(x^2-4\\right)^2} = \\cfrac{x^4-12x^2}{\\left(x^2-4\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"298\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u0437\u0430\u0442\u0435\u043c \u0440\u0435\u0448\u0430\u0435\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\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-50df15bb48cacf8f031b640994661e47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^2 - \\left(x^4-12x^2\\right)\\cdot 2\\left(x^2-4\\right)\\cdot 2x }{ \\left(\\left(x^2-4\\right)^2 \\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"483\" style=\"vertical-align: -33px;\"><\/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-3b05b5f09c2adbfead593df2cdf2ad29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^2 - \\left(x^4-12x^2\\right)\\cdot 4x\\left(x^2-4\\right) }{\\left(x^2-4\\right)^4 }\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"461\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u0441\u0435 \u0447\u043b\u0435\u043d\u044b \u0443\u043c\u043d\u043e\u0436\u0430\u044e\u0442\u0441\u044f \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-1e0f0d9a63183e28c50a5cedcddeddd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x^2-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<p> . \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u044c \u0434\u0440\u043e\u0431\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-92e1aa280d06bf8b58045845d5e21f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^{\\cancel{2}} - \\left(x^4-12x^2\\right)\\cdot 4x\\cancel{\\left(x^2-4\\right)} }{\\left(x^2-4\\right)^{\\cancelto{3}{4}} }\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"458\" style=\"vertical-align: -20px;\"><\/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-a912eff3359969b6ffbef96a3f16932d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right) - \\left(x^4-12x^2\\right)\\cdot 4x}{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"386\" style=\"vertical-align: -20px;\"><\/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-8bc35bdd2b70bbac52fa0f24bbefa261_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{4x^5-16x^3-24x^3+96x - \\left(4x^5-48x^3\\right) }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"381\" style=\"vertical-align: -20px;\"><\/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-045971f71cc11ced77ea0df9f2c514fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{4x^5-16x^3-24x^3+96x - 4x^5+48x^3 }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"365\" style=\"vertical-align: -20px;\"><\/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-3144a0aa00ee8ec427752f05f0fac40c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{8x^3+96x  }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"145\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043a\u043e\u0440\u043d\u0438 \u0432\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\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-f618f4961c18c45be60fc496ad4896e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(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-e8ed519add27a4d51c75b49179e632ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{8x^3+96x  }{\\left(x^2-4\\right)^3 }=0\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"109\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0435\u0440\u043c\u0438\u043d<\/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-d8590a90fab5aef55d7b45cd89e01943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2-4\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"70\" style=\"vertical-align: -7px;\"><\/p>\n<p> \u042d\u0442\u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u0442 \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u0441\u0435\u0439 \u043b\u0435\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438, \u0447\u0442\u043e\u0431\u044b \u043c\u044b \u043c\u043e\u0433\u043b\u0438 \u0443\u043c\u043d\u043e\u0436\u0438\u0442\u044c \u0435\u0435 \u043d\u0430 \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-b5c0d1e44accc3b68a67598f5c4d834c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3+96x =0\\cdot \\left(x^2-4\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"193\" style=\"vertical-align: -7px;\"><\/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-4c52a7448e4acc67488ef5747cc3bed9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3+96x =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u044b\u0434\u0435\u043b\u0438\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-4f2884a1c9b8dabf6ea5323f2ac71b2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x(8x^2+96)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\"><\/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-31adba554b44aa92fd7227506440ccaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x\\cdot(8x^2+96) =0 \\longrightarrow \\begin{cases} \\bm{x =0} \\\\[2ex] 8x^2+96=0 \\ \\longrightarrow \\ x^2=\\cfrac{-96}{8}} = -12 \\ \\longrightarrow \\ x= \\sqrt{-12} \\ \\color{red}\\bm{\\times} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"635\" 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-635e2ffa452a5a66a4bcacb0e111c5ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= \\sqrt{-12}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"81\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0435\u0442, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0438\u0437 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u043d\u0435\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043a\u043e\u0440\u043d\u044f.<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 \u0432\u0441\u0435 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438, \u0442\u043e \u0435\u0441\u0442\u044c \u0442\u043e\u0447\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f (x=-2 \u0438 x=+2) \u0438 \u0442\u0435, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u043e\u043a\u0440\u0430\u0449\u0430\u044e\u0442 \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e (x=0): <\/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-2-0-2.webp\" alt=\"\" class=\"wp-image-2399\" width=\"385\" height=\"75\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0418 \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0437\u043d\u0430\u043a \u0432\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0432 \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, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439. \u0418\u0442\u0430\u043a, \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 \u0438 \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0437\u043d\u0430\u043a \u0438\u043c\u0435\u0435\u0442 \u0432\u0442\u043e\u0440\u0430\u044f \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-3b5618d1ab96a078d50507f45155595b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-3)=\\cfrac{8(-3)^3+96(-3)  }{\\left((-3)^2-4\\right)^3 } = \\cfrac{-504}{125}=-4,03 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"408\" style=\"vertical-align: -20px;\"><\/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-e2e868f1f815d4155a187c55b004cc13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-1)=\\cfrac{8(-1)^3+96(-1)  }{\\left((-1)^2-4\\right)^3 } = \\cfrac{-104}{-27}=3,85 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"394\" style=\"vertical-align: -20px;\"><\/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-3814746f7f9e8aa3920e3f84cd0ff0eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(1)=\\cfrac{8\\cdot1^3+96\\cdot 1  }{\\left(1^2-4\\right)^3 } = \\cfrac{104}{-27}=-3,85 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"348\" style=\"vertical-align: -20px;\"><\/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-54d98824f72954de12bc065471a610e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(3)=\\cfrac{8\\cdot 3^3+96\\cdot 3  }{\\left(3^2-4\\right)^3 } = \\cfrac{504}{125}=4,03 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"329\" style=\"vertical-align: -20px;\"><\/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-2-0-2-courbure.webp\" alt=\"\" class=\"wp-image-2568\" width=\"383\" height=\"129\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u0415\u0441\u043b\u0438 \u0432\u0442\u043e\u0440\u0430\u044f \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\u044b\u043f\u0443\u043a\u043b\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-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> , \u0438 \u0435\u0441\u043b\u0438 \u0432\u0442\u043e\u0440\u0430\u044f \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 \u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> . \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u0438 \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0440\u0430\u0432\u043d\u044b:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0412\u044b\u043f\u0443\u043a\u043b\u044b\u0439<\/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-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd739761b2dc845594c0a0696a240c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-2,0)\\cup (2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>\u0412\u043e\u0433\u043d\u0443\u0442\u044b\u0439<\/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-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong> <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e741ac026627200772655094f921f26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,-2)\\cup (0,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" 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\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u0424\u0443\u043d\u043a\u0446\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-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0438\u043c\u0435\u0435\u0442 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u043a\u0440\u0430\u0439\u043d\u043e\u0441\u0442\u044c \u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p> . \u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5b03f70f64c85542b93152492ab8bd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cup )\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0432 \u044d\u0442\u043e\u0442 \u0436\u0435 \u043c\u043e\u043c\u0435\u043d\u0442. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u043c \u0438\u043b\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u0432 \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/span> <\/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\"> \u041f\u0443\u0441\u0442\u044c \u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f \u0444\u0443\u043d\u043a\u0446\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-d2bb599fff4b55075f6de7628a35f822_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cup)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0412<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u0442.\u0435.<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6e1c4b76e92a6fd3dd8c16dfb2ca8cf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(3)>0&#8243; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;19&#8243; width=&#187;74&#8243; style=&#187;vertical-align: -5px;&#187;><\/p>\n<p> .<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043a\u0440\u0430\u0439\u043d\u0438\u0439<\/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-2176aa2efb23d1fbd644eff672465ff0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=3}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p> <strong>\u042d\u0442\u043e \u043c\u0438\u043d\u0438\u043c\u0443\u043c<\/strong> , \u0442\u0430\u043a \u043a\u0430\u043a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8cfc4aa0fa7cede2c69561e8b65a6991_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u042d\u0442\u043e \u043f\u043e\u0437\u0438\u0442\u0438\u0432\u043d\u043e.<\/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 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\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 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u043d\u0430 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438? \u0412\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0412\u043e\u0433\u043d\u0443\u0442\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0433\u0440\u0430\u0444\u0438\u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0438\u043c\u0435\u0435\u0442 \u0444\u043e\u0440\u043c\u0443 \u0433\u043e\u0440\u044b, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%b2%d0%be%d0%b3%d0%bd%d1%83%d1%82%d0%be%d1%81%d1%82%d0%b8-%d0%b8-%d0%b2%d1%8b%d0%bf%d1%83%d0%ba%d0%bb%d0%be%d1%81%d1%82%d0%b8-%d0%ba%d1%80%d0%b8%d0%b2\/\"> <span class=\"screen-reader-text\">\u0412\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 (\u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0430)<\/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":[6],"tags":[],"class_list":["post-47","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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