{"id":48,"date":"2023-09-17T10:55:22","date_gmt":"2023-09-17T10:55:22","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%82%d0%be%d1%87%d0%ba%d0%b8-%d0%bf%d0%b5%d1%80%d0%b5%d0%b3%d0%b8%d0%b1%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/"},"modified":"2023-09-17T10:55:22","modified_gmt":"2023-09-17T10:55:22","slug":"%d1%82%d0%be%d1%87%d0%ba%d0%b8-%d0%bf%d0%b5%d1%80%d0%b5%d0%b3%d0%b8%d0%b1%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%82%d0%be%d1%87%d0%ba%d0%b8-%d0%bf%d0%b5%d1%80%d0%b5%d0%b3%d0%b8%d0%b1%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/","title":{"rendered":"\u0422\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0432\u0441\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0438 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-puntos-de-inflexion-de-una-funcion\"><\/span> \u041a\u0430\u043a\u043e\u0432\u044b \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0422\u043e\u0447\u043a\u0430\u043c\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u0435\u043d\u044f\u0435\u0442 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443, \u0442\u043e \u0435\u0441\u0442\u044c \u0432 \u0442\u043e\u0447\u043a\u0435 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u0435\u043d\u044f\u0435\u0442 \u0444\u043e\u0440\u043c\u0443 \u0441 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u043d\u0430 \u0432\u044b\u043f\u0443\u043a\u043b\u0443\u044e \u0438\u043b\u0438 \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442.<\/strong> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-saber-si-una-funcion-tiene-un-punto-de-inflexion\"><\/span> \u041a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u0435\u0441\u0442\u044c \u043b\u0438 \u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u0443\u0437\u043d\u0430\u0442\u044c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/p>\n<div style=\"background-color:#FFF3E0; padding-top: 23px; padding-bottom: 0.5px; padding-right: 35px; padding-left: 30px; border-radius:30px;\">\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 <strong>\u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430<\/strong> \u0432 \u0442\u043e\u0447\u043a\u0430\u0445, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u043e\u043a\u0440\u0430\u0449\u0430\u044e\u0442 \u0435\u0435 \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e, \u0430 \u0435\u0435 \u0442\u0440\u0435\u0442\u044c\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043d\u0435 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\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-0deb5fc13e20049e642bdc68a5c35a8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l}f''(a)=0\\\\[2ex]f'''(a)\\neq 0\\end{array}\\right\\} \\quad \\bm{\\longrightarrow} \\quad x=a \\text{ es un punto de inflexi\\'on}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"405\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<p> \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0442\u0440\u0435\u0442\u044c\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\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-37bed97da1ec1d3c4eefd018c3d75650_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u0438 \u0442\u0440\u0435\u0442\u044c\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \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-379ab2238c65191bfc16a940f5a7375d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"119\" 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-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-d65ebc63b5e7fa667d5e25e40448942c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'''(x)=6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\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 \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-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-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> \u0422\u043e\u0433\u0434\u0430 \u0442\u043e\u0447\u043a\u0430 x=0 \u0431\u0443\u0434\u0435\u0442 \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0435\u0441\u043b\u0438 \u0442\u0440\u0435\u0442\u044c\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043d\u0435 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e. \u0412 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0442\u0440\u0435\u0442\u044c\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432\u0441\u0435\u0433\u0434\u0430 \u0440\u0430\u0432\u043d\u0430 6.<\/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-4e11c7a68a7805dd5d27f43c4d332d11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'''(0)=6\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, x=0 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-estudiar-la-curvatura-y-hallar-los-puntos-de-inflexion-de-una-funcion\"><\/span> \u041a\u0430\u043a \u0438\u0437\u0443\u0447\u0438\u0442\u044c \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0438 \u043d\u0430\u0439\u0442\u0438 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043f\u043e\u0432\u043e\u0440\u043e\u0442\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a. \u041e\u0434\u043d\u0430\u043a\u043e \u043c\u044b \u043e\u0431\u044b\u0447\u043d\u043e \u0441\u043a\u043b\u043e\u043d\u043d\u044b \u0438\u0437\u0443\u0447\u0430\u0442\u044c \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0442\u043e \u0435\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \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, \u0430 \u0437\u0430\u0442\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430.<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0447\u0435\u0440\u0435\u0437 \u0435\u0435 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443, \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;\"><strong>\u0417\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<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0422\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430<\/strong> \u2014 \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u0435\u043d\u044f\u0435\u0442 \u0444\u043e\u0440\u043c\u0443 \u0441 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u043d\u0430 \u0432\u043e\u0433\u043d\u0443\u0442\u0443\u044e \u0438\u043b\u0438 \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442.<\/span><\/li>\n<\/ol>\n<\/div>\n<p> \u0427\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 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u044d\u0442\u043e\u0439 \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u044b, \u043c\u044b \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e \u0440\u0435\u0448\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u043d\u0438\u0436\u0435:<\/p>\n<ul>\n<li> \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0438 \u043d\u0430\u0439\u0434\u0438\u0442\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \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:<\/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-1c8c498c40649602a0573f686b30f46d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4-6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" 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. \u042d\u0442\u043e \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \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, \u0442\u043e \u0435\u0441\u0442\u044c \u044d\u0442\u043e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\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-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\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0438\u0437\u0443\u0447\u0438\u0442\u044c, \u0432 \u043a\u0430\u043a\u0438\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 \u043e\u043d\u0430 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\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-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> .<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \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-7602daac91808a70b1b980676921f6d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4-6x^2 \\ \\longrightarrow \\ f'(x)= 4x^3-12x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"314\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u0430\u043b\u0435\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\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-53a801c5309b20a5ad6b5b5981fde19e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=4x^3-12x \\ \\longrightarrow \\ f''(x)= 12x^2-12\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"330\" 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-2ce944968a13592d994b5d76185e2ae9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^2-12=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"107\" 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-e5db8208512c91e36a1ece605a967be0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^2=12\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" 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-22930ba9e08e00b2388ec1a767443147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=\\cfrac{12}{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" 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-959000af33497314f9a59a9bed2a19c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" 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-003a71cb0ec797dfcd0cca915b03a795_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^2}=\\sqrt{1}\" 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-fa2841908f61047e2edf3a8b60ab5962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" 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> , \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0432\u0441\u0435 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \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-1-1.webp\" alt=\"\" class=\"wp-image-2596\" width=\"312\" height=\"79\" 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-3268d2c9fa6d3192f84d914bb9163680_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=12x^2-12\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"141\" 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-290ddf1ed5524d38fa79c593052cca0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-2) = 12\\cdot (-2)^2-12 =36 \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"287\" 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-dc8cd9fb09f76eeb69fdeda81a49c674_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(0) = 12\\cdot 0^2-12 = -12 \\  \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"259\" 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-f35d5dc33f0ffbdf9b02b856ff70e1fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(2) = 12\\cdot 2^2-12=36 \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"245\" 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-1-1-positif-negatif-positif.webp\" alt=\"\" class=\"wp-image-2597\" width=\"315\" height=\"140\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \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 \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-9f11bddd110e2869bf60761b066d16c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,-1) \\cup (1,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" 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-3c8937d362a3ba07fa9068381afe74a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-1,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043f\u0440\u0438 x=-1 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u043a \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=-1 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <strong>.<\/strong> \u0410 \u043f\u0440\u0438 x=1 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u043a \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=1 \u0442\u0430\u043a\u0436\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438 \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 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0443 Y \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0435\u0433\u0438\u0431\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-da3f60ecfa8eb1666821a1a26a103825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-1)=(-1)^4-6(-1)^2 = 1-6 \\cdot 1 = -5 \\ \\longrightarrow \\ (-1,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"437\" 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-d8544d4624c7030bd065734e22efd792_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=1^4-6\\cdot 1^2 = 1-6 \\cdot 1 = -5 \\ \\longrightarrow \\ (1,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"367\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u043e\u0432\u043e\u0440\u043e\u0442\u043d\u044b\u043c\u0438 \u043c\u043e\u043c\u0435\u043d\u0442\u0430\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u041f\u043e\u0432\u043e\u0440\u043e\u0442\u043d\u044b\u0435 \u043c\u043e\u043c\u0435\u043d\u0442\u044b:<\/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-2576ee14a4d19421150e7b696f83c31f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-1,-5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>\u0418<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2220ee8c6ddd44fd21975caeace894d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,-5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0438\u0436\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438\u0437\u0443\u0447\u0430\u0435\u043c\u043e\u0439 \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\/points-dinflexion-dune-fonction.webp\" alt=\"\u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\" class=\"wp-image-2598\" width=\"457\" height=\"493\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u043d\u043e \u0438\u0437 \u0433\u0440\u0430\u0444\u0438\u043a\u0430, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u0434\u0435\u0442 \u0438\u0437 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\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-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> \u0431\u044b\u0442\u044c \u0432\u043e\u0433\u043d\u0443\u0442\u044b\u043c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-69b1c740acf744d34bf12f12dedabf65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cap)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u041e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1bf0660982e8c9a229e9bd39f6a71341_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-1,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0442\u0430\u043a \u043a\u0430\u043a \u0435\u0433\u043e \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0430 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f. \u0410 \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u0434\u0435\u0442 \u043e\u0442 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-69b1c740acf744d34bf12f12dedabf65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cap)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0431\u044b\u0442\u044c \u0432\u044b\u043f\u0443\u043a\u043b\u044b\u043c<\/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> \u041e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97e5c7dfce41ba68b73f6246d1554039_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<p> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-puntos-de-inflexion\"><\/span> \u0420\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u043f\u043e\u0432\u043e\u0440\u043e\u0442\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f<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> \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\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, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\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-175df6eaf87d8a34e6c7f52ffcf4dde7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = xe^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" 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\"> \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. \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 (x), \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u0438\u0437 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b, \u0438 \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 ( <sup>ex<\/sup> ), \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0442\u0430\u043a\u0436\u0435 \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. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \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\"> \u0422\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\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, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \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-996eb43fbe77816d37d7bfa7f35e1e63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=1 \\cdot e^x+ x \\cdot e^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"162\" 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-a3d95f44577d8448674370dd53e02726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=e^x +xe^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u0430\u043b\u0435\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\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-956f25a80e8ccc50a8888c8adc1e134e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= e^x + 1 \\cdot e^x+ x \\cdot e^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"204\" 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-551f7a75a4b0338b53e7decaf413e976_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=e^x +e^x + xe^x  = 2e^x +xe^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u043b\u043e\u0436\u0438\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0440\u0430\u0432\u043d\u043e\u0439 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-dc9977afe23305adab3b6c332e4232bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2e^x+xe^x= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"107\" 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-bf04b8cea9a81435b3106d94a8bba193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e^x(2+x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" 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-e4b369d45e5559de1f7069b49db2d173_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle e^x\\cdot(2+x) =0 \\longrightarrow \\begin{cases} e^x=0 \\ \\color{red}\\bm{\\times}\\color{black}  \\\\[2ex] 2+x=0 \\ \\longrightarrow \\ x= - 2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"350\" 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, \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0434\u0430\u0442\u044c 0. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \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-0108040ee23df4da2db681c9ffb2decc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e^x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" 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\"> \u0412\u0441\u0435 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0435 \u043e\u0441\u043e\u0431\u044b\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \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-2-1.webp\" alt=\"\" class=\"wp-image-2602\" width=\"199\" height=\"78\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \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. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u043e\u0437\u044c\u043c\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 \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\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \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-e5deb7fd9574dd41f2571836c131654d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-3)= 2e^{-3} +(-3)\\cdot e^{-3} = 0,1 - 0,15 = -0,05\\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"442\" 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-fc38d25b16bf677962f89d5562265437_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(0)= 2e^0 +0\\cdot e^0 = 2 \\cdot 1 + 0 \\cdot 1 =2+0= 2 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"404\" 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-2-courbure.webp\" alt=\"\" class=\"wp-image-2603\" width=\"201\" height=\"135\" 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-087de0300a010f86265ccd4f69d8570e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" 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-266c9537df2a55b66ad1c2868728fddf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,-2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0441 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u043d\u0430 \u0432\u044b\u043f\u0443\u043a\u043b\u0443\u044e \u043f\u0440\u0438 x=-2, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=-2 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/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 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \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 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0443 Y \u0442\u043e\u0447\u043a\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-3aee30bfafb6ab70bdc2bc672a61a780_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2) = (-2)\\cdot e^{-2} =-2e^{-2} \\ \\longrightarrow \\ (-2,-2e^{-2})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"362\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435, \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c\u0438 \u043f\u043e\u0432\u043e\u0440\u043e\u0442\u043d\u044b\u043c\u0438 \u043c\u043e\u043c\u0435\u043d\u0442\u0430\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u041f\u043e\u0432\u043e\u0440\u043e\u0442\u043d\u044b\u0435 \u043c\u043e\u043c\u0435\u043d\u0442\u044b:<\/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-676ef444bb4f5ed3116dc104f451295d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-2,-2e^{-2})}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"92\" 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 \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 \u0438 \u043d\u0430\u0439\u0434\u0438\u0442\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \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<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u0435\u043d\u044f\u0435\u0442 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0432 \u0442\u0440\u0435\u0445 \u0442\u043e\u0447\u043a\u0430\u0445, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0435 \u0431\u0443\u0434\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0442\u0440\u0438 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430: x=-2, x=0 \u0438 x=2. \u041e\u0434\u043d\u0430\u043a\u043e, \u0445\u043e\u0442\u044f \u0438 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u044b \u043f\u0440\u0438 x=-2 \u0438 x=+2, \u044d\u0442\u043e \u043d\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \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. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043f\u0440\u0438 x=0 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u044b, \u0438 \u044d\u0442\u043e \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0438\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=0 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041e\u0441\u0442\u0430\u0451\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0443 Y \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\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-ba8c4d5b9201e0971f4a036ea6b0f887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(0)=\\frac{0^3}{0^2-4} =\\frac{0}{-4}=0\\ \\longrightarrow \\ (0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"279\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u043e\u0440\u043e\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0430\u0447\u0430\u043b\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442:<\/p>\n<p class=\"has-text-align-center\"> <strong>\u041f\u043e\u0432\u043e\u0440\u043e\u0442\u043d\u044b\u0435 \u043c\u043e\u043c\u0435\u043d\u0442\u044b:<\/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-2c790019bd70403eba876c59c82c0f9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" 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> \u041c\u044b \u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e \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-a047814c11fd2f3da04a21a9d489da58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3+ax^2+bx+c\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u043f\u0440\u043e\u0439\u0442\u0438 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1542b88e9f0c10166380ce26011f4d14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<p> , \u0438\u043c\u0435\u0435\u0442 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c \u0432<\/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> \u0438 \u043f\u043e\u0432\u043e\u0440\u043e\u0442\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3976ff8b81cbf5060581dc2ccd19c5c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> . \u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u043e\u0439 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0438 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432.<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0357ced152d91599aefcf60b48861b74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a, b\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\"><\/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-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> . <\/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 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0432 \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-2a9b760ebc3dca7954a7b6656a30c8cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0417\u043d\u0430\u0447\u0438\u0442 \u044d\u0442\u043e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9c643154cd44808d027e645761f5921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(2)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> . \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\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 \u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2a9b760ebc3dca7954a7b6656a30c8cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0438 \u043c\u044b \u0443\u0441\u0442\u0430\u043d\u0430\u0432\u043b\u0438\u0432\u0430\u0435\u043c \u0435\u0433\u043e \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-a452ebc56e45c70455952e82f24bc213_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^3+ax^2+bx+c \\ \\longrightarrow \\  f'(x)=3x^2+2ax+b\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"413\" 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-88269f2eaaf1326ed88cec634a839505_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2+2ax+b \\ \\longrightarrow \\ f''(x)= 6x+2a\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"344\" 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-428d0d2aa58a4f0bee3155e72060aee4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} f''(2)=6\\cdot 2+2a\\\\[2ex] f''(2)=0\\end{array} \\right\\} \\longrightarrow 6\\cdot 2+2a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"301\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u0440\u0435\u0448\u0430\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 \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-08eaf911dd0de580da1db41c3a8a25d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\cdot 2+2a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"103\" 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-4127c25ec4efd2c7b05070600fca7040_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12+2a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" 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-21de66a92427317edcb4a2475fcbb3f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2a=-12\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-313aff06eefaaf9af361841519334293_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=\\cfrac{-12}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"75\" 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-81f76a9a366a0e75d702129c2a0cf565_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{a=-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/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 \u0431\u0443\u0434\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-f82d6e87e465fabd9889eec2ed94b7ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3+ax^2+bx+c \\ \\xrightarrow{a \\ = \\ -6}\\ f(x)=x^3-6x^2+bx+c\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\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-5a0a069e4bb53cf46ff9611c104b13f0_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> , \u041a\u043e\u0442\u043e\u0440\u043e\u0435 \u0437\u043d\u0430\u0447\u0438\u0442 \u0447\u0442\u043e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ba772a3114b7ee64171db5cc258b34b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(1)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<p> . \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \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 \u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a0a069e4bb53cf46ff9611c104b13f0_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> \u0438 \u043c\u044b \u0443\u0441\u0442\u0430\u043d\u0430\u0432\u043b\u0438\u0432\u0430\u0435\u043c \u0435\u0433\u043e \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-347dc6fd1ded234104fd25f2e787c4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-6x^2+bx+c \\ \\longrightarrow \\ f'(x)=3x^2-12x+b\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"412\" 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-561b9c2aa6ba34d90df560c5a97e3a92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} f'(1)=3\\cdot 1^2-12\\cdot 1+b\\\\[2ex] f'(1)=0\\end{array} \\right\\} \\longrightarrow 3\\cdot 1^2-12\\cdot 1+b=0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u0440\u0435\u0448\u0430\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0433\u043e b: <\/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-3362d7ea7f2e10163031aaa7ed824c52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3\\cdot 1^2-12\\cdot 1+b=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"161\" 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-2e6fe2c6a93ee7e3cda9732cced98c54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3 \\cdot 1 -12 + b = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"132\" 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-a73022570e08c83b3c148066c88595fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3 -12 + b = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"110\" 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-4cb3fc18020c592a99e0d3db8a57955f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b=+12-3\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"93\" 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-a73ce8b725442e911ac1a46aceb20457_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{b=9}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\"><\/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 \u0431\u0443\u0434\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-9a7549d54df3579050c71e4e06eeb053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-6x^2+bx+c \\ \\xrightarrow{b \\ = \\ 9} \\ f(x)=x^3-6x^2+9x+c\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"455\" style=\"vertical-align: -5px;\"><\/p>\n<\/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 \u0433\u043e\u0432\u043e\u0440\u044f\u0442 \u043d\u0430\u043c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 (3,1). \u042d\u0442\u043e \u0441\u043a\u0430\u0437\u0430\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-27c6a831fde145aea6f8d30359e84f03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p> . \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u044d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 c:<\/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-b496beb319ccab8292181ec1387ba9f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} f(3)=3^3-6\\cdot 3^2+9\\cdot3+c \\\\[2ex] f(3)=1 \\end{array} \\right\\} \\longrightarrow 3^3-6\\cdot 3^2+9\\cdot 3+c = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"467\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u0440\u0435\u0448\u0430\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\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-4586bc1b16791cf732fc00ee37db4357_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" 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-410da829676625edf3c06a986ce96acb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3^3-6\\cdot 3^2+9\\cdot 3+c = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"190\" 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-f860f41d277c58f8714e45bda45c1a27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27-6\\cdot 9+27+c = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"170\" 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-74e9b29b4c5de8c37cad4b293f196fca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27-54+27+c = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"157\" 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-41daca67d3a063fdd50d16d2a3e43bb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c=1-27+54-27\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" 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-5825f757c3f04143a8c5598e0468cb33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{c=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\"><\/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 \u0431\u0443\u0434\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-dd400bd7ca4f75d8ae12b7aa9e9680ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-6x^2+9x+c \\ \\xrightarrow{c \\ = \\ 1} \\ f(x)=x^3-6x^2+9x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"457\" style=\"vertical-align: -5px;\"><\/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, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0432\u0441\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0438 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041a\u0430\u043a\u043e\u0432\u044b \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438? \u0422\u043e\u0447\u043a\u0430\u043c\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u0435\u043d\u044f\u0435\u0442 \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443, \u0442\u043e \u0435\u0441\u0442\u044c \u0432 \u0442\u043e\u0447\u043a\u0435 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 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