{"id":755,"date":"2021-02-15T15:20:21","date_gmt":"2021-02-15T15:20:21","guid":{"rendered":"https:\/\/otus.ru\/journal\/?p=755"},"modified":"2026-09-02T14:47:03","modified_gmt":"2026-09-02T14:47:03","slug":"grafiki-issledovanie-postroenie-algoritm","status":"publish","type":"post","link":"https:\/\/otus.ru\/journal\/grafiki-issledovanie-postroenie-algoritm\/","title":{"rendered":"\u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430: \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c"},"content":{"rendered":"<p>\u0427\u0442\u043e\u0431\u044b \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0438\u0441\u0441\u043b\u0435\u0434\u0443\u044e\u0442: \u043d\u0430\u0445\u043e\u0434\u044f\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044f\u043c\u0438, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438 \u0437\u043d\u0430\u043a\u043e\u043f\u043e\u0441\u0442\u043e\u044f\u043d\u0441\u0442\u0432\u0430, \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f, \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b. \u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 &#8212; \u043f\u043e\u043b\u043d\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u043e \u0448\u0430\u0433\u0430\u043c \u0438 \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0441\u043e \u0441\u0432\u043e\u0434\u043d\u043e\u0439 \u0442\u0430\u0431\u043b\u0438\u0446\u0435\u0439 \u0438 \u0438\u0442\u043e\u0433\u043e\u0432\u044b\u043c \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u043c.<\/p>\n<div class=\"oj-toc\" style=\"background:#f6f6f6;border-radius:8px;padding:14px 20px;margin:20px 0\">\n<p><strong>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435<\/strong><\/p>\n<ol>\n<li><a href=\"#s1\">\u0427\u0442\u043e \u0434\u0430\u0451\u0442 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/a><\/li>\n<li><a href=\"#s2\">\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/a><\/li>\n<li><a href=\"#s3\">\u041f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440: f(x) = x\u00b3 \u2212 3x<\/a><\/li>\n<li><a href=\"#s4\">\u041a\u0430\u043a \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0432 Python (\u0441 \u043e\u0442\u043c\u0435\u0442\u043a\u043e\u0439 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a)<\/a><\/li>\n<li><a href=\"#s5\">\u0412\u044b\u0432\u043e\u0434\u044b<\/a><\/li>\n<li><a href=\"#s6\">FAQ<\/a><\/li>\n<\/ol>\n<\/div>\n<h2 id=\"s1\">\u0427\u0442\u043e \u0434\u0430\u0451\u0442 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/h2>\n<p>\u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0434\u0430\u0451\u0442 \u043d\u0430\u0431\u043e\u0440 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a \u0438 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u043e\u0432, \u043f\u043e \u043a\u043e\u0442\u043e\u0440\u043e\u043c\u0443 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c <strong>\u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u044d\u0441\u043a\u0438\u0437<\/strong> \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0438 \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438 \u043e\u043d \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c. \u0412\u0430\u0436\u043d\u043e \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c: \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u043d\u0430\u0431\u043e\u0440 \u0442\u043e\u0447\u0435\u043a \u0438 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432 \u0437\u0430\u0434\u0430\u0451\u0442 \u043d\u0435 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0443\u044e \u043a\u0440\u0438\u0432\u0443\u044e &#8212; \u043c\u0435\u0436\u0434\u0443 \u043e\u043f\u043e\u0440\u043d\u044b\u043c\u0438 \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u043e\u0432\u0435\u0441\u0442\u0438 \u0440\u0430\u0437\u043d\u044b\u0435 \u043b\u0438\u043d\u0438\u0438 \u0441 \u0442\u0435\u043c\u0438 \u0436\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c\u0438. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0446\u0435\u043b\u044c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f &#8212; \u0441\u043e\u0433\u043b\u0430\u0441\u043e\u0432\u0430\u043d\u043d\u044b\u0439, \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c\u044b\u0439 \u044d\u0441\u043a\u0438\u0437, \u0430 \u043d\u0435 \u00ab\u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0439\u00bb \u0440\u0438\u0441\u0443\u043d\u043e\u043a.<\/p>\n<h2 id=\"s2\">\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/h2>\n<ol>\n<li><strong>\u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/strong><\/li>\n<li><strong>\u0427\u0451\u0442\u043d\u043e\u0441\u0442\u044c \u0438 \u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u043d\u043e\u0441\u0442\u044c<\/strong> (f(\u2212x) = f(x) &#8212; \u0447\u0451\u0442\u043d\u0430\u044f; f(\u2212x) = \u2212f(x) &#8212; \u043d\u0435\u0447\u0451\u0442\u043d\u0430\u044f).<\/li>\n<li><strong>\u0422\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044f\u043c\u0438<\/strong> (f(0); \u0440\u0435\u0448\u0438\u0442\u044c f(x) = 0).<\/li>\n<li><strong>\u041f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438 \u0437\u043d\u0430\u043a\u043e\u043f\u043e\u0441\u0442\u043e\u044f\u043d\u0441\u0442\u0432\u0430<\/strong> (\u0433\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430\/\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430).<\/li>\n<li><strong>\u041f\u0435\u0440\u0432\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f &#8212; \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u0435, \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u0435, \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b.<\/strong> \u041a\u0430\u043d\u0434\u0438\u0434\u0430\u0442\u044b \u0432 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b &#8212; \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438, \u0433\u0434\u0435 f\u2032(x) = 0 <em>\u0438\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442, \u0430 \u0441\u0430\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430<\/em>, \u043f\u043b\u044e\u0441 \u0433\u0440\u0430\u043d\u0438\u0446\u044b \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0430. \u041a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u043d\u0430 \u0431\u044b\u0442\u044c \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u043c &#8212; \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c <strong>\u0441\u043c\u0435\u043d\u0443 \u0437\u043d\u0430\u043a\u0430<\/strong> f\u2032: \u0441 \u043f\u043b\u044e\u0441\u0430 \u043d\u0430 \u043c\u0438\u043d\u0443\u0441 &#8212; \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c, \u0441 \u043c\u0438\u043d\u0443\u0441\u0430 \u043d\u0430 \u043f\u043b\u044e\u0441 &#8212; \u043c\u0438\u043d\u0438\u043c\u0443\u043c.<\/li>\n<li><strong>\u0412\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f &#8212; \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431.<\/strong> \u041d\u0443\u043b\u044c f\u2033 &#8212; \u043b\u0438\u0448\u044c \u043a\u0430\u043d\u0434\u0438\u0434\u0430\u0442; \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0442\u0430\u043c, \u0433\u0434\u0435 <strong>\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438<\/strong> (\u0437\u043d\u0430\u043a f\u2033). \u0413\u0434\u0435 f\u2033 &gt; 0 &#8212; \u0433\u0440\u0430\u0444\u0438\u043a \u0432\u044b\u0433\u043d\u0443\u0442 \u0432\u043d\u0438\u0437, \u0433\u0434\u0435 f\u2033 &lt; 0 &#8212; \u0432\u044b\u0433\u043d\u0443\u0442 \u0432\u0432\u0435\u0440\u0445.<\/li>\n<li><strong>\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b<\/strong> (\u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 \u0440\u0430\u0437\u0440\u044b\u0432\u0430; \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435\/\u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 &#8212; \u043f\u043e \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044e \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438).<\/li>\n<li><strong>\u0421\u0432\u043e\u0434\u043d\u0430\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a.<\/strong><\/li>\n<\/ol>\n<h2 id=\"s3\">\u041f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440: f(x) = x\u00b3 \u2212 3x<\/h2>\n<ul>\n<li><strong>\u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f:<\/strong> \u0432\u0441\u044f \u0447\u0438\u0441\u043b\u043e\u0432\u0430\u044f \u043f\u0440\u044f\u043c\u0430\u044f.<\/li>\n<li><strong>\u0427\u0451\u0442\u043d\u043e\u0441\u0442\u044c:<\/strong> f(\u2212x) = \u2212x\u00b3 + 3x = \u2212f(x) &#8212; \u043d\u0435\u0447\u0451\u0442\u043d\u0430\u044f, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u044f \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043d\u0430\u0447\u0430\u043b\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442.<\/li>\n<li><strong>\u041f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f:<\/strong> f(0) = 0; f(x) = 0 \u043f\u0440\u0438 x(x\u00b2 \u2212 3) = 0, \u0442\u043e \u0435\u0441\u0442\u044c x = 0, \u00b1\u221a3.<\/li>\n<li><strong>\u041f\u0435\u0440\u0432\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f:<\/strong> f\u2032(x) = 3x\u00b2 \u2212 3 = 3(x\u00b2 \u2212 1); \u043d\u0443\u043b\u0438 \u043f\u0440\u0438 x = \u00b11.<\/li>\n<li><strong>\u041c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u044c:<\/strong> f\u2032 &gt; 0 \u043d\u0430 (\u2212\u221e; \u22121) \u0438 (1; \u221e) &#8212; \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442; f\u2032 &lt; 0 \u043d\u0430 (\u22121; 1) &#8212; \u0443\u0431\u044b\u0432\u0430\u0435\u0442. \u0417\u043d\u0430\u0447\u0438\u0442 x = \u22121 &#8212; \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c (f(\u22121) = 2), x = 1 &#8212; \u043c\u0438\u043d\u0438\u043c\u0443\u043c (f(1) = \u22122).<\/li>\n<li><strong>\u041f\u0435\u0440\u0435\u0433\u0438\u0431:<\/strong> f\u2033(x) = 6x. f\u2033 &lt; 0 \u043f\u0440\u0438 x &lt; 0 \u0438 f\u2033 &gt; 0 \u043f\u0440\u0438 x &gt; 0 &#8212; \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 x = 0 &#8212; \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 (0; 0).<\/li>\n<li><strong>\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u043d\u0435\u0442.<\/strong><\/li>\n<\/ul>\n<figure>\n<table border=\"1\" cellpadding=\"6\" style=\"border-collapse:collapse\">\n<tr>\n<th>x<\/th>\n<th>(\u2212\u221e; \u22121)<\/th>\n<th>\u22121<\/th>\n<th>(\u22121; 0)<\/th>\n<th>0<\/th>\n<th>(0; 1)<\/th>\n<th>1<\/th>\n<th>(1; \u221e)<\/th>\n<\/tr>\n<tr>\n<td>f\u2032<\/td>\n<td>+<\/td>\n<td>0<\/td>\n<td>\u2212<\/td>\n<td>\u2212<\/td>\n<td>\u2212<\/td>\n<td>0<\/td>\n<td>+<\/td>\n<\/tr>\n<tr>\n<td>f\u2033<\/td>\n<td>\u2212<\/td>\n<td>\u2212<\/td>\n<td>\u2212<\/td>\n<td>0<\/td>\n<td>+<\/td>\n<td>+<\/td>\n<td>+<\/td>\n<\/tr>\n<tr>\n<td>\u0432\u044b\u0432\u043e\u0434<\/td>\n<td>\u0432\u043e\u0437\u0440.<\/td>\n<td>max<\/td>\n<td>\u0443\u0431\u044b\u0432.<\/td>\n<td>\u043f\u0435\u0440\u0435\u0433\u0438\u0431<\/td>\n<td>\u0443\u0431\u044b\u0432.<\/td>\n<td>min<\/td>\n<td>\u0432\u043e\u0437\u0440.<\/td>\n<\/tr>\n<\/table><figcaption>\u0421\u0432\u043e\u0434\u043d\u0430\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 f(x) = x\u00b3 \u2212 3x.<\/figcaption><\/figure>\n<figure><img decoding=\"async\" src=\"https:\/\/otus.ru\/journal\/wp-content\/uploads\/2026\/09\/grafik-funkcii-x3-3x-issledovanie.png\" alt=\"\u0413\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 x^3-3x \u0441 \u043a\u043e\u0440\u043d\u044f\u043c\u0438, \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430\u043c\u0438 \u0438 \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430\"\/><figcaption>\u0413\u0440\u0430\u0444\u0438\u043a f(x) = x\u00b3 \u2212 3x \u0441 \u043e\u0442\u043c\u0435\u0447\u0435\u043d\u043d\u044b\u043c\u0438 \u043a\u043e\u0440\u043d\u044f\u043c\u0438 \u00b1\u221a3 \u0438 0, \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c (\u22121; 2), \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u043c (1; \u22122) \u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u043e\u043c (0; 0).<\/figcaption><\/figure>\n<h2 id=\"s4\">\u041a\u0430\u043a \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0432 Python (\u0441 \u043e\u0442\u043c\u0435\u0442\u043a\u043e\u0439 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a)<\/h2>\n<pre><code>import numpy as np\nimport matplotlib.pyplot as plt\n\nf = lambda x: x**3 - 3*x\nx = np.linspace(-2.5, 2.5, 400)\nplt.plot(x, f(x))\nfor px in [-np.sqrt(3), 0, np.sqrt(3)]:\n    plt.scatter(px, 0, color=\"green\")   # \u043a\u043e\u0440\u043d\u0438\nplt.scatter(-1, f(-1), color=\"red\")     # \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\nplt.scatter(1, f(1), color=\"red\")       # \u043c\u0438\u043d\u0438\u043c\u0443\u043c\nplt.scatter(0, 0, color=\"orange\")       # \u043f\u0435\u0440\u0435\u0433\u0438\u0431\nplt.grid(True); plt.show()<\/code><\/pre>\n<h2 id=\"s5\">\u0412\u044b\u0432\u043e\u0434\u044b<\/h2>\n<ul>\n<li>\u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 &#8212; \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044f\u043c\u0438, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u043e\u0432 \u0437\u043d\u0430\u043a\u043e\u043f\u043e\u0441\u0442\u043e\u044f\u043d\u0441\u0442\u0432\u0430, \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u043e\u0432 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f, \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u0438 \u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442, \u043f\u043e \u043a\u043e\u0442\u043e\u0440\u044b\u043c \u0441\u0442\u0440\u043e\u0438\u0442\u0441\u044f \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u044d\u0441\u043a\u0438\u0437 \u0433\u0440\u0430\u0444\u0438\u043a\u0430.<\/li>\n<li>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0438\u0434\u0451\u0442 \u043f\u043e \u0448\u0430\u0433\u0430\u043c: \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0447\u0451\u0442\u043d\u043e\u0441\u0442\u044c \u0438 \u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u043d\u043e\u0441\u0442\u044c, \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044f\u043c\u0438, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438 \u0437\u043d\u0430\u043a\u043e\u043f\u043e\u0441\u0442\u043e\u044f\u043d\u0441\u0442\u0432\u0430, \u043f\u0435\u0440\u0432\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f, \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f, \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0441\u0432\u043e\u0434\u043d\u0430\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a.<\/li>\n<li>\u042d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b \u0438\u0449\u0443\u0442 \u0441\u0440\u0435\u0434\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a (f\u2032 = 0 \u0438\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442, \u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430) \u0438 \u0433\u0440\u0430\u043d\u0438\u0446 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0430, \u043d\u043e \u043f\u043e\u0434\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c \u0442\u043e\u043b\u044c\u043a\u043e \u0441\u043c\u0435\u043d\u0430 \u0437\u043d\u0430\u043a\u0430 f\u2032: \u0441 \u043f\u043b\u044e\u0441\u0430 \u043d\u0430 \u043c\u0438\u043d\u0443\u0441 &#8212; \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c, \u0441 \u043c\u0438\u043d\u0443\u0441\u0430 \u043d\u0430 \u043f\u043b\u044e\u0441 &#8212; \u043c\u0438\u043d\u0438\u043c\u0443\u043c.<\/li>\n<li>\u041d\u0443\u043b\u044c \u0432\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 &#8212; \u043b\u0438\u0448\u044c \u043a\u0430\u043d\u0434\u0438\u0434\u0430\u0442 \u0432 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430; \u043f\u0435\u0440\u0435\u0433\u0438\u0431 \u0435\u0441\u0442\u044c \u0442\u0430\u043c, \u0433\u0434\u0435 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0437\u043d\u0430\u043a f\u2033 (\u043f\u0440\u0438 f\u2033 &gt; 0 \u0433\u0440\u0430\u0444\u0438\u043a \u0432\u044b\u0433\u043d\u0443\u0442 \u0432\u043d\u0438\u0437, \u043f\u0440\u0438 f\u2033 &lt; 0 &#8212; \u0432\u044b\u0433\u043d\u0443\u0442 \u0432\u0432\u0435\u0440\u0445).<\/li>\n<li>\u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u043d\u0430\u0431\u043e\u0440 \u0442\u043e\u0447\u0435\u043a \u0438 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432 \u0437\u0430\u0434\u0430\u0451\u0442 \u043d\u0435 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0443\u044e \u043a\u0440\u0438\u0432\u0443\u044e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f &#8212; \u0441\u043e\u0433\u043b\u0430\u0441\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u0438 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c\u044b\u0439 \u044d\u0441\u043a\u0438\u0437 \u0433\u0440\u0430\u0444\u0438\u043a\u0430, \u0430 \u043d\u0435 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0439 \u0440\u0438\u0441\u0443\u043d\u043e\u043a.<\/li>\n<li>\u0414\u043b\u044f f(x) = x\u00b3 \u2212 3x \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f: \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435\u0447\u0451\u0442\u043d\u0430\u044f, \u043a\u043e\u0440\u043d\u0438 0 \u0438 \u00b1\u221a3, \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c (\u22121; 2), \u043c\u0438\u043d\u0438\u043c\u0443\u043c (1; \u22122), \u043f\u0435\u0440\u0435\u0433\u0438\u0431 \u0432 \u0442\u043e\u0447\u043a\u0435 (0; 0), \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u043d\u0435\u0442; \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0432 Python \u0441 matplotlib \u0441 \u043e\u0442\u043c\u0435\u0442\u043a\u043e\u0439 \u044d\u0442\u0438\u0445 \u0442\u043e\u0447\u0435\u043a \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u0442 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0432\u044b\u0432\u043e\u0434.<\/li>\n<\/ul>\n<div class=\"oj-cta\" style=\"background:#fbf4e4;border-left:4px solid #c9962b;border-radius:8px;padding:16px 20px;margin:24px 0\">\n<p>\u0422\u0430\u043a \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u043d\u0430\u044f \u0447\u0430\u0441\u0442\u044c \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u0442 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0432\u044b\u0432\u043e\u0434: \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u0441 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u043c\u0438 \u043a\u043e\u0440\u043d\u044f\u043c\u0438, \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430\u043c\u0438 \u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u043e\u043c. \u0412\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044e \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 matplotlib \u0441\u0438\u0441\u0442\u0435\u043c\u043d\u043e \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u044e\u0442 \u043d\u0430 \u043a\u0443\u0440\u0441\u0430\u0445 Otus \u043f\u043e Python \u0438 \u0430\u043d\u0430\u043b\u0438\u0437\u0443 \u0434\u0430\u043d\u043d\u044b\u0445 &#8212; \u0444\u043e\u0440\u043c\u0430\u0442 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043d\u0430 \u0431\u0435\u0441\u043f\u043b\u0430\u0442\u043d\u044b\u0445 <a href=\"https:\/\/otus.ru\/events\/?utm_source=oj&#038;utm_medium=article&#038;utm_campaign=grafiki&#038;utm_content=events\">\u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0445 \u0443\u0440\u043e\u043a\u0430\u0445 Otus<\/a>. \u0423\u0433\u043b\u0443\u0431\u0438\u0442\u044c\u0441\u044f \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0443 \u043f\u043e\u0434 \u0430\u043d\u0430\u043b\u0438\u0437 \u0434\u0430\u043d\u043d\u044b\u0445 \u043f\u043e\u043c\u043e\u0433\u0430\u0435\u0442 \u043a\u0443\u0440\u0441 <a href=\"https:\/\/otus.ru\/lessons\/math-ds-advanced\/?utm_source=oj&#038;utm_medium=article&#038;utm_campaign=grafiki&#038;utm_content=course\">\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0434\u043b\u044f Data Science<\/a>.<\/p>\n<\/div>\n<h2 id=\"s6\">FAQ<\/h2>\n<p><strong>\u0421 \u0447\u0435\u0433\u043e \u043d\u0430\u0447\u0430\u0442\u044c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435?<\/strong> \u0421 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/p>\n<p><strong>\u041a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b?<\/strong> \u041d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 (f\u2032 = 0 \u0438\u043b\u0438 \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442) \u0438 \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c \u0441\u043c\u0435\u043d\u0443 \u0437\u043d\u0430\u043a\u0430 f\u2032.<\/p>\n<p><strong>\u0417\u0430\u0447\u0435\u043c \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f?<\/strong> \u041f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0438 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 (\u0447\u0435\u0440\u0435\u0437 \u0441\u043c\u0435\u043d\u0443 \u0437\u043d\u0430\u043a\u0430 f\u2033).<\/p>\n<p><em>\u0421\u043c\u0435\u0436\u043d\u044b\u0435 \u0442\u0435\u043c\u044b \u0432 \u0436\u0443\u0440\u043d\u0430\u043b\u0435:<\/em> <a href=\"https:\/\/otus.ru\/journal\/integraly-ot-a-do-ya\/\">\u0418\u043d\u0442\u0435\u0433\u0440\u0430\u043b: \u0447\u0442\u043e \u044d\u0442\u043e, \u0432\u0438\u0434\u044b \u0438 \u043a\u0430\u043a \u0441\u0447\u0438\u0442\u0430\u0442\u044c<\/a>, <a href=\"https:\/\/otus.ru\/journal\/logarifmy-opisanie-i-graficheskoe-izobrazhenie\/\">\u041b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u044b: \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u0438 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0427\u0442\u043e\u0431\u044b \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0438\u0441\u0441\u043b\u0435\u0434\u0443\u044e\u0442: \u043d\u0430\u0445\u043e\u0434\u044f\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044f\u043c\u0438, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438 \u0437\u043d\u0430\u043a\u043e\u043f\u043e\u0441\u0442\u043e\u044f\u043d\u0441\u0442\u0432\u0430, \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f, \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b. \u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 &#8212; \u043f\u043e\u043b\u043d\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u043e \u0448\u0430\u0433\u0430\u043c \u0438 \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0441\u043e \u0441\u0432\u043e\u0434\u043d\u043e\u0439 \u0442\u0430\u0431\u043b\u0438\u0446\u0435\u0439 \u0438 \u0438\u0442\u043e\u0433\u043e\u0432\u044b\u043c \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u043c. \u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435 \u0427\u0442\u043e \u0434\u0430\u0451\u0442 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u041f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440: f(x) [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":757,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[44],"class_list":["post-755","post","type-post","status-publish","format-standard","has-post-thumbnail","","category-polza","tag-matematika"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u0427\u0442\u043e\u0431\u044b \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0438\u0441\u0441\u043b\u0435\u0434\u0443\u044e\u0442: \u043d\u0430\u0445\u043e\u0434\u044f\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044f\u043c\u0438, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438 \u0437\u043d\u0430\u043a\u043e\u043f\u043e\u0441\u0442\u043e\u044f\u043d\u0441\u0442\u0432\u0430, \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b, \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f, \u0432\u044b\u043f\u0443\u043a\u043b\u043e\u0441\u0442\u044c \u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b. \u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 - \u043f\u043e\u043b\u043d\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u043e \u0448\u0430\u0433\u0430\u043c \u0438 \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0441\u043e \u0441\u0432\u043e\u0434\u043d\u043e\u0439 \u0442\u0430\u0431\u043b\u0438\u0446\u0435\u0439 \u0438 \u0438\u0442\u043e\u0433\u043e\u0432\u044b\u043c \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u043c. \u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435 \u0427\u0442\u043e \u0434\u0430\u0451\u0442 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u041f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440: f(x)\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"A. Pavlenko\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/otus.ru\/journal\/grafiki-issledovanie-postroenie-algoritm\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.1.1\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/otus.ru\\\/journal\\\/grafiki-issledovanie-postroenie-algoritm\\\/#article\",\"name\":\"\\u0418\\u0441\\u0441\\u043b\\u0435\\u0434\\u043e\\u0432\\u0430\\u043d\\u0438\\u0435 \\u0444\\u0443\\u043d\\u043a\\u0446\\u0438\\u0438 \\u0438 \\u043f\\u043e\\u0441\\u0442\\u0440\\u043e\\u0435\\u043d\\u0438\\u0435 \\u0433\\u0440\\u0430\\u0444\\u0438\\u043a\\u0430: \\u043f\\u043e\\u0448\\u0430\\u0433\\u043e\\u0432\\u044b\\u0439 \\u0430\\u043b\\u0433\\u043e\\u0440\\u0438\\u0442\\u043c OTUS\",\"headline\":\"\\u0418\\u0441\\u0441\\u043b\\u0435\\u0434\\u043e\\u0432\\u0430\\u043d\\u0438\\u0435 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