{"id":325,"date":"2023-07-06T08:31:48","date_gmt":"2023-07-06T08:31:48","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86%d0%b0-%d0%b3%d0%b5%d1%81%d1%81%d0%b8%d0%b0%d0%bd%d0%b0-2x2-3x3\/"},"modified":"2023-07-06T08:31:48","modified_gmt":"2023-07-06T08:31:48","slug":"%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86%d0%b0-%d0%b3%d0%b5%d1%81%d1%81%d0%b8%d0%b0%d0%bd%d0%b0-2x2-3x3","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86%d0%b0-%d0%b3%d0%b5%d1%81%d1%81%d0%b8%d0%b0%d0%bd%d0%b0-2x2-3x3\/","title":{"rendered":"\u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0433\u0435\u0441\u0441\u0435 (\u0438\u043b\u0438 \u0433\u0435\u0441\u0441\u0435)"},"content":{"rendered":"<p>\u042d\u0442\u0430 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430, \u0431\u0435\u0437\u0443\u0441\u043b\u043e\u0432\u043d\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u043b\u043d\u044b\u043c \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435\u043c \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435. \u0417\u0434\u0435\u0441\u044c \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435, \u0441\u043f\u043e\u0441\u043e\u0431\u044b \u0435\u0435 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438 \u0438 \u0434\u0430\u0436\u0435 \u0435\u0441\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0434\u043b\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0438. \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0437\u043d\u0430\u0442\u044c, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0438 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u0430 \u0442\u0430\u043a\u0436\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d\u0430 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439. \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0443\u0442\u0438\u043b\u0438\u0442\u044b \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435.<\/p>\n<h2 class=\"wp-block-heading\"> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435?<\/h2>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 (\u0438\u043b\u0438 \u0433\u0435\u0441\u0441\u0438\u0430\u043d\u0430) \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>\u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435<\/strong> \u2014 \u044d\u0442\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0430\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 n \u00d7 n, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u0430\u044f \u0438\u0437 \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u0432\u0442\u043e\u0440\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 n \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445.<\/p>\n<p> \u042d\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0442\u0430\u043a\u0436\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430 \u043a\u0430\u043a \u0433\u0435\u0441\u0441\u0438\u0430\u043d \u0438\u043b\u0438 \u0434\u0430\u0436\u0435 \u0432 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0443\u0447\u0435\u0431\u043d\u0438\u043a\u0430\u0445 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0435\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442\u043d\u043e\u0439. \u041d\u043e \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u044b\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0435\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0442\u044c \u2014 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c: <\/p>\n<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\/formule-matricielle-hessienne.webp\" alt=\"\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u0438\u043b\u0438 \u0413\u0435\u0441\u0441\u0438\u0430\u043d\u0430\" class=\"wp-image-2445\" width=\"541\" height=\"345\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u0432\u0441\u0435\u0433\u0434\u0430 \u0431\u0443\u0434\u0435\u0442 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439, \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u043d\u0430 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0435\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 3 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u0431\u0443\u0434\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c 3\u00d73.<\/p>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, <strong>\u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0428\u0432\u0430\u0440\u0446\u0430<\/strong> (\u0438\u043b\u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u041a\u043b\u0435\u0440\u043e) \u0433\u043e\u0432\u043e\u0440\u0438\u0442, \u0447\u0442\u043e \u043f\u043e\u0440\u044f\u0434\u043e\u043a \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0442.\u0435. \u0447\u0430\u0441\u0442\u0438\u0447\u043d\u043e \u0432\u044b\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\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-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u0442\u043e\u0433\u0434\u0430 \u043f\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\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-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u0441\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043a \u0447\u0430\u0441\u0442\u0438\u0447\u043d\u043e\u043c\u0443 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044e \u043f\u043e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u0442\u043e\u0433\u0434\u0430 \u0443\u0432\u0430\u0436\u0435\u043d\u0438\u0435<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> .<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e5cc28564c40c6588680df48d8255ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x_i\\partial x_j} = \\cfrac{\\partial^2 f}{\\partial x_j\\partial x_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"133\" style=\"vertical-align: -18px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439<\/strong> \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439, \u0438\u043b\u0438, \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u043e\u043d\u0430 \u043e\u0431\u043b\u0430\u0434\u0430\u0435\u0442 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0435\u0439, \u043e\u0441\u044c\u044e \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0435\u0435 \u0433\u043b\u0430\u0432\u043d\u0430\u044f \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u044c.<\/p>\n<p> \u041b\u044e\u0431\u043e\u043f\u044b\u0442\u043d\u043e, \u0447\u0442\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043d\u0430\u0437\u0432\u0430\u043d\u0430 \u0432 \u0447\u0435\u0441\u0442\u044c \u041b\u044e\u0434\u0432\u0438\u0433\u0430 \u041e\u0442\u0442\u043e \u0413\u0435\u0441\u0441\u0435, \u043d\u0435\u043c\u0435\u0446\u043a\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 XIX \u0432\u0435\u043a\u0430, \u0432\u043d\u0435\u0441\u0448\u0435\u0433\u043e \u043e\u0447\u0435\u043d\u044c \u0432\u0430\u0436\u043d\u044b\u0439 \u0432\u043a\u043b\u0430\u0434 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u044b.<\/p>\n<h2 class=\"wp-block-heading\"> \u041f\u0440\u0438\u043c\u0435\u0440 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435<\/h2>\n<p> \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 2 \u00d7 2:<\/p>\n<ul>\n<li> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 (1,0) \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03bcc33e393ddc95defdc3cc04da35c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  f(x,y)=y^4+x^3+3x^2+ 4y^2 -4xy -5y +8\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"348\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fd57722dfa592f129cac21ba8f183e05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial x} = 3x^2 +6x -4y\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"152\" 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-1847d0b9ecd032b396d64ac27e5e3eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial y} = 4y^3+8y -4x -5\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"181\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u043c \u043f\u0435\u0440\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0432\u0441\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-294ce075a54a240e012d30770fa10e3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x^2} = 6x +6\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"102\" 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-895c605e3c401f96a0a9b07ea105522c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial y^2} =12y^2 +8\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"118\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ea4b2979928198e9fb91592d9e38874_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x \\partial y} = \\cfrac{\\partial^2 f}{\\partial y \\partial x}= -4\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"153\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0442\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043d\u0430\u0439\u0442\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446 2\u00d72:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-926f350fe0ac3184ec0b563b57fd6041_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (x,y)=\\begin{pmatrix}\\cfrac{\\partial^2 f}{\\partial x^2} &amp; \\cfrac{\\partial^2 f}{\\partial x \\partial y} \\\\[4ex] \\cfrac{\\partial^2 f}{\\partial y \\partial x} &amp; \\cfrac{\\partial^2 f}{\\partial y^2} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"111\" width=\"215\" 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-b7f3d45918645a5b6019896ed45eda75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (x,y)=\\begin{pmatrix}6x +6 &amp;-4 \\\\[2ex] -4 &amp; 12y^2+8 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"246\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435, \u043e\u0446\u0435\u043d\u0435\u043d\u043d\u0430\u044f \u0432 \u0442\u043e\u0447\u043a\u0435 (1,0), \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-bdccfc61f7befe6c75f66c8a4658f3e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (1,0)=\\begin{pmatrix}6(1) +6 &amp;-4 \\\\[2ex] -4 &amp; 12(0)^2+8 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"270\" style=\"vertical-align: 0px;\"><\/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\/exemple-matrice-hessienne-de-dimension-22152.webp\" alt=\"\u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0448\u0442\u0430\u043c\u043f\u043e\u0432 \u0438\u0437 \u043c\u0435\u0448\u043a\u043e\u0432\u0438\u043d\u044b \u0438\u043b\u0438 \u043c\u0435\u0448\u043a\u043e\u0432\u0438\u043d\u044b\" class=\"wp-image-2487\" width=\"230\" height=\"80\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043c\u0430\u0442\u0440\u0438\u0446 \u0413\u0435\u0441\u0441\u0435<\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u0434\u0432\u0443\u043c\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 (1,1): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d1e63eb1506d471fb8fdbc0e6db8de0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  f(x,y)=x^2y+y^2x\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"151\" 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__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\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 \u043d\u0430\u0439\u0442\u0438 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \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-9786ccaea4ad9305eb8b50d98f7f2626_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial x} = 2xy+y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"111\" 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-7b68a8a666732d228ad06ebd8bade063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial y} = x^2+2yx\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"112\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0443\u0436\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u043f\u0435\u0440\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435, \u043f\u0440\u0438\u0441\u0442\u0443\u043f\u0430\u0435\u043c \u043a \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u0432\u0441\u0435\u0445 \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef3e5008f32d204cae79f8faceafb6ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x^2} = 2y\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"70\" 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-0e3f3f68ddab03ad22776b84f441cb7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial y^2} =2x\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"71\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e6383bbe85e851dd1e573981b52a0158_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x \\partial y} = \\cfrac{\\partial^2 f}{\\partial y \\partial x}=2x+2y\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"188\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c: <\/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\/exercice-resolu-de-matrice-hessian-22152-1.webp\" alt=\"\u0420\u0435\u0448\u0435\u043d\u043d\u043e\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u0441 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0413\u0435\u0441\u0441\u0435 \u0438\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0413\u0435\u0441\u0441\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c 2\u04452.\" class=\"wp-image-2492\" width=\"290\" height=\"81\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043e\u0441\u0442\u0430\u0435\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 (1,1): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e5353c0229942269e07455047284f92b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (1,1)=\\begin{pmatrix}2\\cdot 1 &amp;2 \\cdot 1+2\\cdot 1 \\\\[1.5ex] 2\\cdot 1+2\\cdot 1 &amp; 2\\cdot 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"292\" 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-cf00fccdb37a19388e76b5a84a408d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{H_f (1,1)}=\\begin{pmatrix}\\bm{2} &amp; \\bm{4} \\\\[1.1ex] \\bm{4} &amp; \\bm{2} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"145\" style=\"vertical-align: 0px;\"><\/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> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0433\u0435\u0441\u0441\u0438\u0430\u043d \u0432 \u0442\u043e\u0447\u043a\u0435 (1,1) \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0434\u0432\u0443\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d577030e612ef7b6ab7b59aea4469539_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  f(x,y)= e^{y\\ln x}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"115\" 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__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\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 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \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-1025a749344fdf59c8c016387b7e2c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial x} = e^{y\\ln x} \\cdot \\cfrac{y}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"110\" 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-2ddfad6313a350d43404b19a2278d771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial y} = e^{y\\ln x} \\cdot \\ln x\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"125\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u043b\u0443\u0447\u0438\u0432 \u043f\u0435\u0440\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \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-edcdf882fac053dc938c4f0d10060d30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x^2} = e^{y\\ln x} \\cdot \\cfrac{y^2}{x^2} - e^{y\\ln x} \\cdot \\cfrac{y}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"219\" 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-1f59a0f7a852311293edd2231235ae7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial y^2} =e^{y\\ln x} \\cdot \\ln ^2 x\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"141\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b760e29d744c2f294cf9cec33d61d1e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x \\partial y}=\\cfrac{\\partial^2 f}{\\partial y \\partial x} =e^{y\\ln x} \\cdot \\cfrac{y}{x}\\cdot \\ln x + e^{y\\ln x}\\cdot \\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"323\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0443\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 2\u00d72: <\/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\/exercice-resolu-de-hesse-de-dimension-22152-1.webp\" alt=\"\u0420\u0435\u0448\u0435\u043d\u043d\u043e\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u0413\u0435\u0441\u0441\u0435 \u0438\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c 2x2\" class=\"wp-image-2516\" width=\"620\" height=\"135\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043e\u0441\u0442\u0430\u0435\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 (1,1): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c316cc61e6d007e5d034274e0f494520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (1,1)=\\begin{pmatrix} e^{1\\ln (1)} \\displaystyle \\cdot \\cfrac{1^2}{1^2} - e^{1\\ln (1)} \\cdot \\cfrac{1}{1^2}&amp; e^{1\\ln (1)} \\cdot \\cfrac{1}{1}\\cdot \\ln (1) + e^{1\\ln (1)}\\cdot \\cfrac{1}{1} \\\\[3ex] e^{1\\ln (1)} \\cdot \\cfrac{1}{1}\\cdot \\ln (1) + e^{1\\ln (1)}\\cdot \\cfrac{1}{1} &amp; e^{1\\ln (1)} \\cdot \\ln ^2 (1) \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"99\" width=\"557\" 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-6e456b856c722a140d73ade63f13ec9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (1,1)=\\begin{pmatrix}e^{0} \\cdot 1 - e^{0} \\cdot 1&amp; e^{0} \\cdot 1\\cdot 0 + e^{0}\\cdot 1 \\\\[2ex] e^{0} \\cdot 1\\cdot 0 + e^{0}\\cdot 1 &amp; e^{0} \\cdot 0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"366\" 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-929fbf6e7f0f90110d11d4ccd51fd51a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (1,1)=\\begin{pmatrix}1 - 1&amp; 0+ 1 \\\\[1.5ex] 0 +1 &amp; 1 \\cdot 0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"206\" 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-ce780ddb8c09515afccfb2da2d842584_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{H_f (1,1)}=\\begin{pmatrix}\\bm{0} &amp; \\bm{1} \\\\[1.1ex] \\bm{1} &amp; \\bm{0} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"145\" style=\"vertical-align: 0px;\"><\/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> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435 \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-b324eec3855aa704cfe7cef3a72713f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,1,\\pi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u0442\u0440\u0435\u043c\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07614221c6aa91fe6591ecfdd7ee064b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  f(x,y,z)= e^{-x}\\cdot \\text{sen}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"189\" 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__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\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 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \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-f3403bbb8643fb0c3f01dc93031683d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial x} = -e^{-x}\\cdot \\text{sen}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"155\" 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-6e77e08ad03b7a454f9a9f5c320d4902_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial y} = ze^{-x}\\cdot \\text{cos}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"149\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-912b948c3339efba02beb10da8853e89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial z} = ye^{-x}\\cdot \\text{cos}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u043b\u0443\u0447\u0438\u0432 \u043f\u0435\u0440\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \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-831ffaaf0208ac80132c58e97c10696d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x^2} =e^{-x}\\cdot \\text{sen}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"149\" 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-f8c77e5f03861145b5370a208642c199_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x \\partial y}=\\cfrac{\\partial^2 f}{\\partial y \\partial x} =-ze^{-x}\\cdot \\text{cos}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"248\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f3a5180d638ffbedb5028da56c5c2b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x \\partial z}=\\cfrac{\\partial^2 f}{\\partial z \\partial x} =-ye^{-x}\\cdot \\text{cos}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"247\" 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-001a3978b472e9085c4658d19e976079_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial y^2} =-z^2e^{-x}\\cdot \\text{sen}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"179\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8c2c222f469c688e41ed773c1721834_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial y \\partial z}=\\cfrac{\\partial^2 f}{\\partial z \\partial y} =e^{-x}\\cdot \\text{cos}(yz)-yze^{-x}\\cdot \\text{sen}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"360\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-98dcbe5198ef8336355c89a80bb981ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial^2 z} = -y^2e^{-x}\\cdot \\text{sen}(yz)\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"179\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a \u0447\u0442\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0443\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 3\u00d73: <\/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\/exemple-de-matrice-de-hesse-en-3-dimensions-32153-1.webp\" alt=\"\u043f\u0440\u0438\u043c\u0435\u0440 \u043c\u0435\u0448\u043a\u043e\u0432\u0438\u043d\u044b \u0438\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u043c\u0435\u0448\u043a\u043e\u0432\u0438\u043d\u044b \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c 3\u04453\" class=\"wp-image-2537\" width=\"857\" height=\"109\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u043c \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u043c\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438 \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-cf0e780dfde4cefb749a03fe14266290_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,1,\\pi):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" 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-4e198192f67babd81228caa53b66e8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f(0,1,\\pi)=\\begin{pmatrix}e^{-0}\\cdot \\text{sen}(1\\pi) &amp; -\\pi e^{-0}\\cdot \\text{cos}(1\\pi) &amp;-1e^{-0}\\cdot \\text{cos}(1\\pi) \\\\[1.5ex] -\\pi e^{-0}\\cdot \\text{cos}(1 \\pi)&amp;-\\pi^2e^{-0}\\cdot \\text{sen}(1 \\pi) &amp;e^{-0}\\cdot \\text{cos}(1 \\pi)-1 \\pi e^{-0}\\cdot \\text{sen}(1 \\pi) \\\\[1.5ex] -1e^{-0}\\cdot \\text{cos}(1 \\pi)&amp; e^{-0}\\cdot \\text{cos}(1 \\pi)-1 \\pi e^{-0}\\cdot \\text{sen}(1 \\pi)&amp; -1^2e^{-0}\\cdot \\text{sen}(1 \\pi) \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"87\" width=\"756\" 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-4ce9c6b4cfcddfb0c2eb51db1189c653_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f(0,1,\\pi)=\\begin{pmatrix}1\\cdot 0 &amp; -\\pi \\cdot 1 \\cdot (-1)&amp;-1\\cdot 1 \\cdot (-1) \\\\[1.5ex] -\\pi \\cdot 1 \\cdot (-1) &amp;-\\pi^2\\cdot 1\\cdot 0 &amp;1 \\cdot (-1)-\\pi \\cdot 1\\cdot 0 \\\\[1.5ex] -1\\cdot 1 \\cdot (-1) &amp; 1\\cdot (-1) - \\pi \\cdot 1\\cdot 0 &amp; -1\\cdot 1 \\cdot 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"527\" style=\"vertical-align: 0px;\"><\/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\/exercice-resolu-de-matrice-hessiana-32153-1.webp\" alt=\"\u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u0440\u0435\u0448\u0430\u0435\u0442\u0441\u044f \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c \u043f\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u0413\u0435\u0441\u0441\u0435 \u0438\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u0413\u0435\u0441\u0441\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c 3x3\" class=\"wp-image-2536\" width=\"291\" height=\"109\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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 4<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 (2,-1,1,-1) \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 4 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cf4dde4cb282d4f494142475a514b6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  f(x,y,z,w)= 2x^3y^4zw^2 - 2y^3w^4+ 3x^2z^2\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"320\" 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__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\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\u044b\u043c \u0448\u0430\u0433\u043e\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \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-d559c24695adc4e5bf25a07162b0b82c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial x} =6x^2y^4zw^2 + 6xz^2\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"175\" 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-7e4b630227d3c64561c2a87f729612b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial y} =8x^3y^3zw^2 - 6y^2w^4\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"186\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c473febcf510cf11a4b30fad46fb3d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial z} = 2x^3y^4w^2 + 6x^2z\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"166\" 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-afc9ac6f800c06919a5bee6d6ea20a38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f}{\\partial w} =4x^3y^4zw - 8y^3w^3\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0430\u0435\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \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-55333bf53a5934f849b6eea4d5a4f64c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x^2} =12xy^4zw^2 + 6z^2\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"174\" 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-ecd6fb72d35cb8c8b09e14dd2337bdfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x \\partial y}=\\cfrac{\\partial^2 f}{\\partial y \\partial x}=24x^2y^3zw^2\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"211\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02885e698f3ae93bbf9515970de030ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x \\partial z}=\\cfrac{\\partial^2 f}{\\partial z \\partial x}=6x^2y^4w^2 + 12xz\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"252\" 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-0a43e7868272e5f9981fd6961c4d2078_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial x \\partial w} = \\cfrac{\\partial^2 f}{\\partial w \\partial x}=12x^2y^4zw\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"212\" 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-fd1617aa3759b2cab9621b821d06f42d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial y^2} =24x^3y^2zw^2 - 12yw^4\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"204\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c019a5c8dd396e6d0ee491d1e96b0f42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial y \\partial z}=\\cfrac{\\partial^2 f}{\\partial y \\partial z}=8x^3y^3w^2\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"191\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-83dc31061c77785623e54e55f39c7bea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial y \\partial w} = \\cfrac{\\partial^2 f}{\\partial w \\partial y}=16x^3y^3zw - 24y^2w^3\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"287\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57b2a8d35948c0ac623709a00922f2a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial^2 z} =6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"78\" 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-260eacc428eb6db6a9a5ad0b7c7e9649_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial z \\partial w} = \\cfrac{\\partial^2 f}{\\partial w \\partial z}=4x^3y^4w\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"192\" 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-7d4cb2a8938dfd2d17cc68cd9260eae5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial^2 f}{\\partial^2 w} =4x^3y^4z - 24y^3w^2\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 4 \u00d7 4, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u0443\u0442\u0435\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0432\u0441\u0435\u0445 \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445, \u0438\u043c\u0435\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u0438\u0434: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-toile-de-jute-ou-matrice-de-toile-de-jute-de-dimension-44.webp\" alt=\"\u043f\u0440\u0438\u043c\u0435\u0440 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043c\u0435\u0448\u043a\u043e\u0432\u0438\u043d\u044b \u0438\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u043c\u0435\u0448\u043a\u043e\u0432\u0438\u043d\u044b \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c 4x4\" width=\"854\" height=\"180\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u043c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u0438\u0445 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 (2,-1,1,-1) \u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-de-hesse-ou-matrice-hessienne-de-dimension-44.webp\" alt=\"\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u0440\u0435\u0448\u0430\u0435\u0442\u0441\u044f \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c \u043f\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u0413\u0435\u0441\u0441\u0435 \u0438\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u0413\u0435\u0441\u0441\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c 4\u04454.\" width=\"457\" height=\"182\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h2 class=\"wp-block-heading\"> \u041a\u0430\u043a \u0443\u0437\u043d\u0430\u0442\u044c, \u043a\u043e\u0433\u0434\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430 \u0438\u043b\u0438 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430?<\/h2>\n<p> \u041a\u0430\u043a \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u043f\u043e\u0437\u0436\u0435, \u0437\u043d\u0430\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e-\u043f\u043e\u043b\u0443\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439, \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e-\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439, \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e-\u043f\u043e\u043b\u0443\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439, \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e-\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0438\u043b\u0438 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439, \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u043b\u0435\u0437\u043d\u043e. \u0418\u0442\u0430\u043a, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u044d\u0442\u043e \u0443\u0437\u043d\u0430\u0442\u044c:<\/p>\n<h3 class=\"wp-block-heading\"> \u041a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 (\u0438\u043b\u0438 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439)<\/h3>\n<p> \u041e\u0434\u0438\u043d \u0438\u0437 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0443\u0437\u043d\u0430\u0442\u044c, \u043a\u0430\u043a\u043e\u0439 \u044d\u0442\u043e \u0442\u0438\u043f \u043c\u0430\u0442\u0440\u0438\u0446\u044b, \u2014 \u043f\u0440\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f) \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435:<\/p>\n<ul>\n<li> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <span style=\"color:#1976d2;\"><strong>\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e-\u043f\u043e\u043b\u0443\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439,<\/strong><\/span> \u0435\u0441\u043b\u0438 \u043e\u043d\u0430 \u0438\u043c\u0435\u0435\u0442 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f), \u0440\u0430\u0432\u043d\u044b\u0435 \u0438 \u0431\u043e\u043b\u044c\u0448\u0438\u0435 \u043d\u0443\u043b\u044f. \u0422\u043e \u0435\u0441\u0442\u044c \u0443 \u043d\u0435\u0433\u043e \u0435\u0441\u0442\u044c \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0438 \u0445\u043e\u0442\u044f \u0431\u044b \u043e\u0434\u043d\u043e, \u0440\u0430\u0432\u043d\u043e\u0435 0:<\/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-21d0afe89f5d1545ccda3d2bd0d8660a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda \\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <span style=\"color:#1976d2;\"><strong>\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439<\/strong><\/span> , \u0435\u0441\u043b\u0438 \u0432\u0441\u0435 \u0435\u0435 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f) \u0438\u0441\u043a\u043b\u044e\u0447\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0431\u043e\u043b\u044c\u0448\u0435 0 (\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435):<\/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-f203da6c7fff0b1487c2084e3d90966b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda > 0&#8243; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;14&#8243; width=&#187;43&#8243; style=&#187;vertical-align: -2px;&#187;><\/p>\n<\/p>\n<ul>\n<li> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <span style=\"color:#1976d2;\"><strong>\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043f\u043e\u043b\u0443\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439,<\/strong><\/span> \u0435\u0441\u043b\u0438 \u043e\u043d\u0430 \u0438\u043c\u0435\u0435\u0442 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f), \u0440\u0430\u0432\u043d\u044b\u0435 \u043d\u0443\u043b\u044e \u0438 \u043c\u0435\u043d\u044c\u0448\u0438\u0435 \u043d\u0435\u0433\u043e. \u0422\u043e \u0435\u0441\u0442\u044c \u043e\u043d \u0438\u043c\u0435\u0435\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0438 \u0445\u043e\u0442\u044f \u0431\u044b \u043e\u0434\u043d\u043e, \u0440\u0430\u0432\u043d\u043e\u0435 0:<\/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-dfdf139bb553d680b38761b565dd3db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda \\leq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <span style=\"color:#1976d2;\"><strong>\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439<\/strong><\/span> , \u0435\u0441\u043b\u0438 \u0432\u0441\u0435 \u0435\u0435 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f) \u043c\u0435\u043d\u044c\u0448\u0435 0 (\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b):<\/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-1fdc8fd3de7c5d7643ca8e4dbfe3704d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda < 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"43\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 <span style=\"color:#1976d2;\"><strong>\u043d\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430<\/strong><\/span> , \u043a\u043e\u0433\u0434\u0430 \u043e\u043d\u0430 \u0438\u043c\u0435\u0435\u0442 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f):<\/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-fa9eea2abe5f790e65f0c5afab8c3adb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda > 0 \\qquad \\lambda <0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"121\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u0421\u0438\u043b\u044c\u0432\u0435\u0441\u0442\u0440\u0430<\/h3>\n<p> \u0414\u0440\u0443\u0433\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0443\u0437\u043d\u0430\u0442\u044c, \u043a \u043a\u0430\u043a\u043e\u043c\u0443 \u0442\u0438\u043f\u0443 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0441\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435, \u2014 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u0421\u0438\u043b\u044c\u0432\u0435\u0441\u0442\u0440\u0430, \u0445\u043e\u0442\u044f \u044d\u0442\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043d\u0430\u043c \u0443\u0437\u043d\u0430\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d\u0430 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439, \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0438\u043b\u0438 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439. \u041d\u043e \u0438\u043d\u043e\u0433\u0434\u0430 \u0435\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043d\u0430\u043c\u043d\u043e\u0433\u043e \u0431\u044b\u0441\u0442\u0440\u0435\u0435, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f, \u043a\u0430\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u043f\u0440\u043e\u0449\u0435. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, <strong>\u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u0421\u0438\u043b\u044c\u0432\u0435\u0441\u0442\u0440\u0430<\/strong> \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<ul>\n<li> \u0415\u0441\u043b\u0438 \u0432\u0441\u0435 \u0433\u043b\u0430\u0432\u043d\u044b\u0435 \u043c\u0438\u043d\u043e\u0440\u044b \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 0, \u044d\u0442\u043e <span style=\"color:#1976d2;\"><strong>\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f<\/strong><\/span> \u043c\u0430\u0442\u0440\u0438\u0446\u0430.<\/li>\n<\/ul>\n<ul>\n<li> \u0415\u0441\u043b\u0438 \u0433\u043b\u0430\u0432\u043d\u044b\u0435 \u043c\u0438\u043d\u043e\u0440\u044b \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u0441 \u0447\u0435\u0442\u043d\u044b\u043c \u0438\u043d\u0434\u0435\u043a\u0441\u043e\u043c \u0431\u043e\u043b\u044c\u0448\u0435 0, \u0430 \u043c\u0438\u043d\u043e\u0440\u044b \u0441 \u043d\u0435\u0447\u0435\u0442\u043d\u044b\u043c \u0438\u043d\u0434\u0435\u043a\u0441\u043e\u043c \u043c\u0435\u043d\u044c\u0448\u0435 0, \u044d\u0442\u043e <span style=\"color:#1976d2;\"><strong>\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f<\/strong><\/span> \u043c\u0430\u0442\u0440\u0438\u0446\u0430.<\/li>\n<\/ul>\n<ul>\n<li> \u0415\u0441\u043b\u0438 \u0432\u0441\u0435 \u0433\u043b\u0430\u0432\u043d\u044b\u0435 \u043c\u0438\u043d\u043e\u0440\u044b \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u043d\u0435 \u0440\u0430\u0432\u043d\u044b 0 \u0438 \u043d\u0438 \u043e\u0434\u043d\u043e \u0438\u0437 \u0434\u0432\u0443\u0445 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u0445 \u0443\u0441\u043b\u043e\u0432\u0438\u0439 \u043d\u0435 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043e, \u044d\u0442\u043e <span style=\"color:#1976d2;\"><strong>\u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f<\/strong><\/span> \u043c\u0430\u0442\u0440\u0438\u0446\u0430. <\/li>\n<\/ul>\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\/majeurs-mineurs-d-une-matrice.webp\" alt=\"\u0433\u043b\u0430\u0432\u043d\u044b\u0435 \u043c\u0438\u043d\u043e\u0440\u044b \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435\" class=\"wp-image-2583\" width=\"417\" height=\"361\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0433\u043b\u0430\u0432\u043d\u044b\u0439 \u043c\u0438\u043d\u043e\u0440 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u0432\u0441\u0435\u0433\u0434\u0430 \u0431\u0443\u0434\u0435\u0442 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0442\u044c \u0441 \u0435\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u0435\u043c. \u0418\u0441\u043a\u043b\u044e\u0447\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0446\u0435\u043b\u044f\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u00ab\u0433\u0435\u0441\u0441\u0438\u0430\u043d\u043e\u043c\u00bb, \u0445\u043e\u0442\u044f \u043c\u044b \u043d\u0435 \u0431\u0443\u0434\u0435\u043c \u0437\u0434\u0435\u0441\u044c \u044d\u0442\u043e\u0433\u043e \u0434\u0435\u043b\u0430\u0442\u044c \u0432\u043e \u0438\u0437\u0431\u0435\u0436\u0430\u043d\u0438\u0435 \u043f\u0443\u0442\u0430\u043d\u0438\u0446\u044b.<\/p>\n<h2 class=\"wp-block-heading\"> \u041a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435<\/h2>\n<p> \u0423\u0437\u043d\u0430\u0432, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435, \u0432\u044b, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e, \u0437\u0430\u0434\u0430\u0435\u0442\u0435\u0441\u044c \u0432\u043e\u043f\u0440\u043e\u0441\u043e\u043c: \u0430 \u0434\u043b\u044f \u0447\u0435\u0433\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u044d\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430?<\/p>\n<p> \u041d\u0443, \u043e\u0434\u043d\u043e \u0438\u0437 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u2014 \u043d\u0430\u0439\u0442\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u0431\u043e\u043b\u0435\u0435 \u0447\u0435\u043c \u043e\u0434\u043d\u043e\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439. \u0412\u043e\u0442 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b:<\/p>\n<ol style=\"color:#1976d2; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#262626;font-weight: normal;\">\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u044e\u0442\u0441\u044f <strong>\u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0438\u043b\u0438  \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438  \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c \u0435\u0435 \u043a 0 \u0438 \u0440\u0435\u0448\u0430\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#262626;font-weight: normal;\">\u0420\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#262626;font-weight: normal;\">\u041a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0435 \u043d\u0430 \u0448\u0430\u0433\u0435 1, \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\u0435. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0441\u0442\u043e\u043b\u044c\u043a\u043e \u043c\u0430\u0442\u0440\u0438\u0446 \u0413\u0435\u0441\u0441\u0435, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0438\u043c\u0435\u044e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044e.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#262626;font-weight: normal;\">\u041c\u044b \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a \u043a\u0430\u043a\u043e\u043c\u0443 \u0442\u0438\u043f\u0443 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0441\u044f \u043a\u0430\u0436\u0434\u0430\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435. \u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d\u043e \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u043c, \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u043c, \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u043c \u0438 \u0442. \u0434.<\/span>\n<ul>\n<li style=\"margin-left:30px; margin-bottom:10px; margin-top:10px\"> <span style=\"color:#262626;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430, \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 <span style=\"color:#1976d2;\"><strong>\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c<\/strong><\/span> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/span><\/li>\n<li style=\"margin-left:30px; margin-bottom:10px\"> <span style=\"color:#262626;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430, \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 <span style=\"color:#1976d2;\"><strong>\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c<\/strong><\/span> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/span><\/li>\n<li style=\"margin-left:30px;\"> <span style=\"color:#262626;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043d\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430, \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <span style=\"color:#1976d2;\"><strong>\u0441\u0435\u0434\u043b\u043e\u0432\u043e\u0439 \u0442\u043e\u0447\u043a\u043e\u0439<\/strong><\/span> .<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u0438\u043c\u0435\u0440 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u0432 \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445<\/h3>\n<p> \u0427\u0442\u043e\u0431\u044b \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f, \u0432\u043e\u0442 \u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0438 \u043a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435:<\/p>\n<ul>\n<li> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u0441\u0435 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445:<\/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-f422cf8ac57ec69b69af091986d534da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  f(x,y)=x^2-y^2+2xy+ 4x-4y\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u0435\u0440\u0432\u043e\u0435, \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c, \u044d\u0442\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0431\u0443\u0434\u0435\u0442 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0442\u044c \u0441 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043e\u043c, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\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-b583925d8f0f0a93afa22c409ae00aa8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\nabla f (x,y)=(2x+2y+4 \\ , \\ -2y+2x-4 )\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"315\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u043c \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438, \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043a 0 \u0438 \u0440\u0435\u0448\u0430\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0b72f879adb6df18c19610c21eba3887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\nabla f (x,y)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" 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-d851eb626a9bd385aec8f68c9df71a39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l} 2x+2y+4 =0 \\\\[2ex] -2y+2x-4=0 \\end{array}\\right\\} \\longrightarrow \\left. \\begin{array}{c} x = 0 \\\\[1.1ex] y = -2 \\end{array}\\right\\} \\longrightarrow \\ (0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"383\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0418\u0442\u0430\u043a, \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u043d\u0430\u0448\u043b\u0438, \u2014 \u044d\u0442\u043e (0,-2).<\/p>\n<p> \u041a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0430\u0439\u0434\u0435\u043d\u0430, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0413\u0435\u0441\u0441\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-702fa5f5c3e3d872e1ec0dad0e3216c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (x,y)=\\begin{pmatrix}2 &amp; 2 \\\\[1.1ex] 2 &amp; -2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"160\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0418, \u043e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435, \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u0430\u044f \u0432 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0435, \u0442\u0430 \u0436\u0435 \u0441\u0430\u043c\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-7b56ffff28d1a9b98c9848891ae924eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f (0,-2)=\\begin{pmatrix}2 &amp; 2 \\\\[1.1ex] 2 &amp; -2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"172\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u0437\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430, \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0435\u043c \u0421\u0438\u043b\u044c\u0432\u0435\u0441\u0442\u0440\u0430. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0440\u0435\u0448\u0430\u0435\u043c \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u043c\u0438\u043d\u043e\u0440\u044b \u043c\u0430\u0442\u0440\u0438\u0446\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-226cf6a18d27a9da300823c13158d56a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}2 \\end{vmatrix} = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"50\" 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-d66efe9fca481475009bb1703939e4f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}2 &amp; 2 \\\\[1.1ex] 2 &amp; -2 \\end{vmatrix} = -8\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"104\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0413\u043b\u0430\u0432\u043d\u044b\u0439 \u043c\u0438\u043d\u043e\u0440 1 (\u043d\u0435\u0447\u0435\u0442\u043d\u044b\u0439) \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u0435\u043d, \u0430 \u0433\u043b\u0430\u0432\u043d\u044b\u0439 \u043c\u0438\u043d\u043e\u0440 2 (\u0447\u0435\u0442\u043d\u044b\u0439) \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u0435\u043d, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u043e \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u044e \u0421\u0438\u043b\u044c\u0432\u0435\u0441\u0442\u0440\u0430 \u044d\u0442\u043e <strong>\u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0430.<\/strong> \u0418, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 (0,-2) \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0441\u0435\u0434\u043b\u043e\u0432\u043e\u0439.<\/strong> <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-119\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u0438 \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435<\/h2>\n<p> \u0414\u0440\u0443\u0433\u043e\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u2014 \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. \u0410 \u044d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u0435:<\/p>\n<p> \u0411\u044b\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-e87f01194fba5ba72beb64431139ece0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A \\subseteq \\mathbb{R}^n\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043d\u0430\u0431\u043e\u0440 \u0438<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4fa98607bbf0ec2af91778a78a134c97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f \\colon A \\to \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"77\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0432\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b, \u0435\u0435 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0441\u0442\u044c \u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0442\u0441\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0413\u0435\u0441\u0441\u0435:<\/p>\n<ul style=\"color:#1976d2; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"> <span style=\"color:#262626;font-weight: normal;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <span style=\"color:#1976d2;\"><strong>\u0432\u044b\u043f\u0443\u043a\u043b\u044b\u043c<\/strong><\/span> \u0432\u043e \u0432\u0441\u0435\u043c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0442\u043e\u0433\u0434\u0430 \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u043e\u0433\u0434\u0430, \u043a\u043e\u0433\u0434\u0430 \u0435\u0433\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043e\u043b\u0443\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430.<\/li>\n<li> <span style=\"color:#262626;font-weight: normal;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span> <span style=\"color:#1976d2;\"><strong>\u0441\u0442\u0440\u043e\u0433\u043e \u0432\u044b\u043f\u0443\u043a\u043b\u0430<\/strong><\/span> \u0432\u043e \u0432\u0441\u0435\u043c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0442\u043e\u0433\u0434\u0430 \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u043e\u0433\u0434\u0430, \u043a\u043e\u0433\u0434\u0430 \u0435\u0433\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430.<\/li>\n<\/ul>\n<p> <strong><span style=\"color:#1976d2;\">\u2713<\/span><\/strong> \u041f\u043e\u044d\u0442\u043e\u043c\u0443, \u0435\u0441\u043b\u0438<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435, \u0433\u0434\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438 \u0442\u0430\u043a\u0436\u0435 \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u0443\u043b\u044c, \u044d\u0442\u0430 \u0442\u043e\u0447\u043a\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u043c \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> .<\/p>\n<ul style=\"color:#1976d2; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"> <span style=\"color:#262626;font-weight: normal;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span> \u0432 \u0446\u0435\u043b\u043e\u043c <span style=\"color:#1976d2;\"><strong>\u0432\u043e\u0433\u043d\u0443\u0442\u044b\u0439<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0442\u043e\u0433\u0434\u0430 \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u043e\u0433\u0434\u0430, \u043a\u043e\u0433\u0434\u0430 \u0435\u0433\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043e\u043b\u0443\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430.<\/li>\n<li> <span style=\"color:#262626;font-weight: normal;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span> \u0432 \u0446\u0435\u043b\u043e\u043c <span style=\"color:#1976d2;\"><strong>\u0441\u0442\u0440\u043e\u0433\u043e \u0432\u043e\u0433\u043d\u0443\u0442\u044b\u0439<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0442\u043e\u0433\u0434\u0430 \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u043e\u0433\u0434\u0430, \u043a\u043e\u0433\u0434\u0430 \u0435\u0433\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430.<\/li>\n<\/ul>\n<p> <strong><span style=\"color:#1976d2;\">\u2713<\/span><\/strong> \u041f\u043e\u044d\u0442\u043e\u043c\u0443, \u0435\u0441\u043b\u0438<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f \u0432 \u0442\u043e\u0447\u043a\u0435, \u0433\u0434\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438 \u0442\u0430\u043a\u0436\u0435 \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u0443\u043b\u044c, \u044d\u0442\u0430 \u0442\u043e\u0447\u043a\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u043c \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> .<\/p>\n<p> \u041d\u0438\u0436\u0435 \u0443 \u0432\u0430\u0441 \u0435\u0441\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u0435\u0449\u0435 \u043e\u0434\u0438\u043d \u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0439 \u0432 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-7\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> \u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/convexite-et-concavite-d-une-fonction-avec-la-matrice-hessienne.webp\" alt=\"\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0432\u044b\u043f\u0443\u043a\u043b\u0443\u044e \u0438\u043b\u0438 \u0432\u043e\u0433\u043d\u0443\u0442\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435\" width=\"411\" height=\"308\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <strong>\u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/concavite-et-convexite-d-une-fonction-avec-la-matrice-hessienne.webp\" alt=\"\u0418\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0438\u043c\u0435\u0435\u0442 \u043f\u0443\u0441\u0442\u043e\u0439 \u0430\u0442\u0440\u0438\u0431\u0443\u0442 ALT; \u0438\u043c\u044f \u0435\u0433\u043e \u0444\u0430\u0439\u043b\u0430 \u2014 \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-\u0441-\u0433\u0435\u0441\u0441\u0438\u0430\u043d\u0441\u043a\u043e\u0439-\u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439-1024x768.jpg\" width=\"411\" height=\"307\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"> \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435<\/h2>\n<p> \u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0441\u043f\u043e\u0441\u043e\u0431\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u043c\u044b \u0443\u0436\u0435 \u0432\u0438\u0434\u0435\u043b\u0438, \u043e\u0434\u043d\u0430\u043a\u043e \u0443 \u043d\u0435\u0435 \u0435\u0441\u0442\u044c \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f. \u041c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c \u0438\u0445 \u043d\u0438\u0436\u0435 \u0434\u043b\u044f \u0441\u0430\u043c\u044b\u0445 \u043b\u044e\u0431\u043e\u043f\u044b\u0442\u043d\u044b\u0445.<\/p>\n<h3 class=\"wp-block-heading\"> \u041f\u043e\u043b\u0438\u043d\u043e\u043c \u0422\u0435\u0439\u043b\u043e\u0440\u0430<\/h3>\n<p> \u0420\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0435 <strong>\u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0430 \u0422\u0435\u0439\u043b\u043e\u0440\u0430<\/strong> \u0434\u043b\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0434\u0432\u0443\u0445 \u0438 \u0431\u043e\u043b\u0435\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043d\u0430\u0447\u0438\u043d\u0430\u0435\u0442\u0441\u044f \u0442\u0430\u043a:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-813a551888f2fe0d61201e11c9cf83da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  T(x) = f(a) + (x-a)^T \\nabla f(a) + \\frac{1}{2}(x-a)^T \\operatorname{H}_f(a)(x-a) + \\ldots\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"475\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u0447\u043b\u0435\u043d\u044b \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0422\u0435\u0439\u043b\u043e\u0440\u0430 \u0437\u0430\u0434\u0430\u044e\u0442\u0441\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0413\u0435\u0441\u0441\u0435, \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c\u043e\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435 \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430.<\/p>\n<h3 class=\"wp-block-heading\"> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0438\u0437 \u043c\u0435\u0448\u043a\u043e\u0432\u0438\u043d\u044b \u0441 \u043e\u043a\u0430\u043d\u0442\u043e\u0432\u043a\u043e\u0439<\/h3>\n<p> \u0414\u0440\u0443\u0433\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u2014 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432 \u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u0432 \u043c\u043d\u043e\u0433\u043e\u043c\u0435\u0440\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-d9f627258270ef54673906bdea5bc47c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x,y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d \u0434\u0440\u0443\u0433\u043e\u0439 \u0440\u043e\u043b\u044c\u044e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-629bf228b3d2b0003d598c1591ec6000_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x,y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"49\" style=\"vertical-align: -5px;\"><\/p>\n<p> . \u0414\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f <strong>\u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435<\/strong> \u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0430:<\/p>\n<p> <strong>\u0428\u0430\u0433 1:<\/strong> \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u041b\u0430\u0433\u0440\u0430\u043d\u0436\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435\u043c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7253e3e437e00468c7dc9b5e4546991a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle L(x,y,\\lambda) = f(x,y)+ \\lambda \\cdot g(x,y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <strong>\u0428\u0430\u0433 2:<\/strong> \u041d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u041b\u0430\u0433\u0440\u0430\u043d\u0436\u0430. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u041b\u0430\u0433\u0440\u0430\u043d\u0436\u0430, \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043a 0 \u0438 \u0440\u0435\u0448\u0430\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-372152b499747854f2da5a2c8c211ce4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\nabla L = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"59\" style=\"vertical-align: -1px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d76d99126f67279a1302a805e2b12e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial L}{\\partial x} = 0 \\qquad \\cfrac{\\partial L}{\\partial y}=0 \\qquad \\cfrac{\\partial L}{\\partial \\lambda}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"240\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> <strong>\u0428\u0430\u0433 3:<\/strong> \u0414\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0439 \u0433\u0435\u0441\u0441\u0438\u0430\u043d, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\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-3d1b2b04de9559a521e6704151c27bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H(f,g) = \\begin{pmatrix}0 &amp; \\cfrac{\\partial g}{\\partial x_1} &amp; \\cfrac{\\partial g}{\\partial x_2} &amp; \\cdots &amp; \\cfrac{\\partial g}{\\partial x_n} \\\\[4ex] \\cfrac{\\partial g}{\\partial x_1} &amp; \\cfrac{\\partial^2 f}{\\partial x_1^2} &amp; \\cfrac{\\partial^2 f}{\\partial x_1\\,\\partial x_2} &amp; \\cdots &amp; \\cfrac{\\partial^2 f}{\\partial x_1\\,\\partial x_n} \\\\[4ex] \\cfrac{\\partial g}{\\partial x_2} &amp; \\cfrac{\\partial^2 f}{\\partial x_2\\,\\partial x_1} &amp; \\cfrac{\\partial^2 f}{\\partial x_2^2} &amp; \\cdots &amp; \\cfrac{\\partial^2 f}{\\partial x_2\\,\\partial x_n} \\\\[3ex] \\vdots &amp; \\vdots &amp; \\vdots &amp; \\ddots &amp; \\vdots \\\\[3ex] \\cfrac{\\partial g}{\\partial x_n} &amp; \\cfrac{\\partial^2 f}{\\partial x_n\\,\\partial x_1} &amp; \\cfrac{\\partial^2 f}{\\partial x_n\\,\\partial x_2} &amp; \\cdots &amp; \\cfrac{\\partial^2 f}{\\partial x_n^2}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"289\" width=\"415\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>\u0428\u0430\u0433 4:<\/strong> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u043c \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d\u0430 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u043c:<\/p>\n<ul>\n<li> \u042d\u0442\u043e \u0431\u0443\u0434\u0435\u0442 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u043f\u0440\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f\u0445<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d208fd391fa57c168dc0f151de829fee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0435\u0441\u043b\u0438 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0435 <em>nm<\/em> (\u0433\u0434\u0435 <em>n<\/em> &#8212; \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u0430 <em>m<\/em> &#8212; \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0439) \u0433\u043b\u0430\u0432\u043d\u044b\u0435 \u043c\u0438\u043d\u043e\u0440\u044b \u0433\u0440\u0430\u043d\u0438\u0447\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435, \u043e\u0446\u0435\u043d\u0435\u043d\u043d\u043e\u0439 \u0432 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0435, \u0438\u043c\u0435\u044e\u0442 \u0447\u0435\u0440\u0435\u0434\u0443\u044e\u0449\u0438\u0435\u0441\u044f \u0437\u043d\u0430\u043a\u0438, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e.<\/li>\n<\/ul>\n<ul>\n<li> \u042d\u0442\u043e \u0431\u0443\u0434\u0435\u0442 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u043f\u0440\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f\u0445<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d208fd391fa57c168dc0f151de829fee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0435\u0441\u043b\u0438 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0435 <em>nm<\/em> (\u0433\u0434\u0435 <em>n<\/em> \u2014 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u0430 <em>m<\/em> \u2014 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0439) \u0433\u043b\u0430\u0432\u043d\u044b\u0435 \u043c\u0438\u043d\u043e\u0440\u044b \u0442\u043e\u0447\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435, \u043e\u0446\u0435\u043d\u0435\u043d\u043d\u043e\u0439 \u0432 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0435, \u0432\u0441\u0435 \u0438\u043c\u0435\u044e\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u043a\u0438.<\/li>\n<\/ul>\n<p> \u0421\u043b\u0435\u0434\u0443\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0432 \u0432\u0438\u0434\u0443, \u0447\u0442\u043e \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b \u0438\u043b\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u043e\u0434\u043d\u043e\u0439 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a \u0434\u0440\u0443\u0433\u043e\u0439 \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043b\u0436\u043d\u044b \u0431\u044b\u0442\u044c \u0442\u0430\u043a\u043e\u0432\u044b\u043c\u0438 \u0434\u043b\u044f \u043d\u0435\u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435 \u0441 \u0433\u0440\u0430\u043d\u0438\u0446\u0430\u043c\u0438 \u043f\u043e\u043b\u0435\u0437\u043d\u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u0437\u0430\u0434\u0430\u0447 \u0442\u0430\u043a\u043e\u0433\u043e \u0442\u0438\u043f\u0430.<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0421\u0432\u044f\u0437\u044c \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f\u043c\u0438<\/h3>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0438\u0430\u043d\u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0432\u0430\u0436\u043d\u044b\u043c\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f\u043c\u0438 \u0438\u043b\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430\u043c\u0438, \u0432 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u043c \u0441 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0438 \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440\u043e\u043c \u041b\u0430\u043f\u043b\u0430\u0441\u0430.<\/p>\n<h4 class=\"wp-block-heading\"> \u0421\u0432\u044f\u0437\u044c \u0441 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430<\/h4>\n<p> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\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-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u2013 <strong>\u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438<\/strong> \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 \u0442\u043e\u0439 \u0436\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-96ab1054f3c447eedac17f9ce04b4606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f = J(\\nabla f)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"97\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<h4 class=\"wp-block-heading\"> \u041e\u043f\u0435\u0440\u0430\u0442\u043e\u0440 \u041b\u0430\u043f\u043b\u0430\u0441\u0430<\/h4>\n<p> \u0421\u043b\u0435\u0434 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u0435\u043d <strong>\u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440\u0443 \u041b\u0430\u043f\u043b\u0430\u0441\u0430<\/strong> :<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-77f16c5285ca6a9ac5899d6e832e9a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle tr( H_f) = \\Delta f\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"101\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> \u042d\u0442\u043e \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u043b\u0435\u0433\u043a\u043e \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u041b\u0430\u043f\u043b\u0430\u0441\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0434\u0438\u0432\u0435\u0440\u0433\u0435\u043d\u0446\u0438\u044f \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 \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-5a3e06f41c5bd51c969601d46507a9c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\Delta f =\\nabla \\cdot (\\nabla f) = (\\nabla \\cdot \\nabla )f = \\nabla^2 f\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0442\u0430\u043a\u043e\u0432\u043e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c7e1ec07ef9178ea4dd56d9cae72d275_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\Delta f = \\cfrac{\\partial ^2 f}{\\partial^2 x_1} +\\cfrac{\\partial ^2 f}{\\partial^2 x_2} + \\cfrac{\\partial ^2 f}{\\partial^2 x_3}+ \\ldots +\\cfrac{\\partial ^2 f}{\\partial^2 x_n}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"310\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> \u0418 \u044d\u0442\u0430 \u0441\u0443\u043c\u043c\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438\u0448\u044c \u0441\u043b\u0435\u0434\u043e\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u044c \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0430.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u042d\u0442\u0430 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430, \u0431\u0435\u0437\u0443\u0441\u043b\u043e\u0432\u043d\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u043b\u043d\u044b\u043c \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435\u043c \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435. \u0417\u0434\u0435\u0441\u044c \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435, \u0441\u043f\u043e\u0441\u043e\u0431\u044b \u0435\u0435 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438 \u0438 \u0434\u0430\u0436\u0435 \u0435\u0441\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0434\u043b\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0438. \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0437\u043d\u0430\u0442\u044c, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0438 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u0430 \u0442\u0430\u043a\u0436\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d\u0430 \u0432\u043e\u0433\u043d\u0443\u0442\u043e\u0439 \u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439. \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0439\u0434\u0435\u0442\u0435 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86%d0%b0-%d0%b3%d0%b5%d1%81%d1%81%d0%b8%d0%b0%d0%bd%d0%b0-2x2-3x3\/\"> <span class=\"screen-reader-text\">\u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0433\u0435\u0441\u0441\u0435 (\u0438\u043b\u0438 \u0433\u0435\u0441\u0441\u0435)<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-325","post","type-post","status-publish","format-standard","hentry","category-7"],"yoast_head":"<!-- This site is optimized 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