{"id":42,"date":"2023-09-17T10:57:01","date_gmt":"2023-09-17T10:57:01","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/"},"modified":"2023-09-17T10:57:01","modified_gmt":"2023-09-17T10:57:01","slug":"%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/","title":{"rendered":"\u4f18\u5316\u95ee\u9898"},"content":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u4e00\u4e0b\u51fd\u6570\u4f18\u5316\u95ee\u9898\u662f\u5982\u4f55\u5206\u9636\u6bb5\u89e3\u51b3\u7684\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u89e3\u51b3\u4f18\u5316\u95ee\u9898\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-problemas-de-optimizacion\"><\/span>\u4ec0\u4e48\u662f\u4f18\u5316\u95ee\u9898\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4f18\u5316\u95ee\u9898<\/strong>\u662f\u5fc5\u987b\u627e\u5230\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u7684\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u4f18\u5316\u95ee\u9898\u6d89\u53ca\u8ba1\u7b97\u5b9a\u4e49\u516c\u53f8\u5229\u6da6\u7684\u51fd\u6570\u7684\u6700\u5927\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-resolver-los-problemas-de-optimizacion\"><\/span>\u5982\u4f55\u89e3\u51b3\u4f18\u5316\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u89e3\u51b3\u529f\u80fd\u4f18\u5316\u95ee\u9898\u7684\u6b65\u9aa4\uff1a<\/p>\n<ol>\n<li><strong>\u8bbe\u7f6e\u9700\u8981\u4f18\u5316\u7684\u529f\u80fd<\/strong>\u3002<\/li>\n<li><strong>\u63a8\u5bfc\u51fa\u8981\u4f18\u5316\u7684\u51fd\u6570\u3002<\/strong><\/li>\n<li>\u627e\u5230\u8981\u4f18\u5316\u7684\u51fd\u6570\u7684<strong>\u5173\u952e\u70b9<\/strong>\u3002\u4e3a\u6b64\uff0c\u60a8\u9700\u8981\u5c06\u51fd\u6570\u7684\u5bfc\u6570\u8bbe\u7f6e\u4e3a\u96f6\u5e76\u6c42\u89e3\u6240\u5f97\u65b9\u7a0b\u3002<\/li>\n<li>\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u5e76<strong>\u786e\u5b9a\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002<\/strong> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-problema-de-optimizacion\"><\/span>\u4f18\u5316\u95ee\u9898\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8003\u8651\u5230\u4f18\u5316\u95ee\u9898\u7684\u7406\u8bba\uff0c\u6211\u4eec\u5c06\u9010\u6b65\u89e3\u51b3\u6b64\u7c7b\u95ee\u9898\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u770b\u5230\u5b83\u4eec\u662f\u5982\u4f55\u8fdb\u884c\u7684\u3002<\/p>\n<ul>\n<li>\u5728\u6240\u6709\u8fb9\u957f\u4e3a 10 \u5398\u7c73\u7684\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u8ba1\u7b97\u8868\u9762\u79ef\u6700\u5927\u7684\u4e00\u4e2a\u7684\u5c3a\u5bf8\u3002<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u4e09\u89d2\u5f62\u7684\u4e00\u4e2a\u5206\u652f\u79f0\u4e3a<em>x<\/em> \uff0c\u53e6\u4e00\u5206\u652f\u79f0\u4e3a<em>y<\/em> \uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-optimisation-probleme.webp\" alt=\"\u4e09\u89d2\u5f62\u4f18\u5316\u95ee\u9898\" class=\"wp-image-2463\" width=\"172\" height=\"156\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p><u style=\"text-decoration-color:#FF9B28;\"><strong><span style=\"color:#1976d2;\">\u6b65\u9aa41\uff1a<\/span><\/strong>\u8bbe\u7f6e\u8981\u4f18\u5316\u7684\u529f\u80fd\u3002<\/u><\/p>\n<p>\u6211\u4eec\u5e0c\u671b\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u6700\u5927\uff0c\u4e09\u89d2\u5f62\u9762\u79ef\u7684\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d1fe72037bfa7f8a181f8f92fdeb5a93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A = \\cfrac{b \\cdot h}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"70\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5728\u6211\u4eec\u7684\u4f8b\u5b50\u4e2d\uff0c\u4e09\u89d2\u5f62\u7684\u5e95\u662f<em>x<\/em> \uff0c\u9ad8\u5ea6<em>\u662f y<\/em> \u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fffb2f09f07fa450174fda22346dc38d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A = \\cfrac{x \\cdot y}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"72\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5df2\u7ecf\u6709\u4e86\u8981\u4f18\u5316\u7684\u51fd\u6570\uff0c\u4f46\u5b83\u4f9d\u8d56\u4e8e\u4e24\u4e2a\u53d8\u91cf\uff0c\u800c\u5b83\u53ea\u80fd\u4f9d\u8d56\u4e8e\u4e00\u4e2a\u53d8\u91cf\u3002\u7136\u800c\uff0c\u58f0\u660e\u544a\u8bc9\u6211\u4eec\u4e24\u6761\u817f\u7684\u603b\u957f\u5ea6\u5fc5\u987b\u4e3a10\u5398\u7c73\u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97009913e60b18a66b47683b142eaa14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+ y = 10\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u4ece\u8fd9\u4e2a\u65b9\u7a0b\u4e2d\u89e3\u51fa<em>y<\/em> \uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9093174098ec3aeadce1fa9dd3724c27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 10 -x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5c06\u8868\u8fbe\u5f0f\u4ee3\u5165\u51fd\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9ab3460a669f3a70a608b0a4c64f520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A = \\cfrac{x \\cdot y}{2} \\ \\xrightarrow{ y \\  = \\ 10 -x } \\ A = \\cfrac{x(10-x)}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"278\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-28b512042d814bf88207c8fb0f9a5543_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x) = \\cfrac{10x-x^2}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"131\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u6709\u4e86\u8ba1\u5212\u7684\u4f18\u5316\u51fd\u6570\uff0c\u5b83\u53ea\u4f9d\u8d56\u4e8e\u4e00\u4e2a\u53d8\u91cf\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u7ee7\u7eed\u4e0b\u4e00\u6b65\u3002<\/p>\n<p><u style=\"text-decoration-color:#FF9B28;\"><strong><span style=\"color:#1976d2;\">\u6b65\u9aa42\uff1a<\/span><\/strong>\u8ba1\u7b97\u5f85\u4f18\u5316\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/u><\/p>\n<p>\u5b83\u662f\u4e00\u4e2a\u6709\u7406\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5e94\u7528\u9664\u6cd5\u5bfc\u6570\u516c\u5f0f\u6765\u63a8\u5bfc\u5b83\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d555f298d7c31d09947787e4d294d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x) = \\cfrac{10x-x^2}{2} \\ \\longrightarrow \\ A'(x) = \\cfrac{(10-2x) \\cdot 2 - (10x-x^2) \\cdot 0}{2^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"467\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00979b72662361213ec4611a28e935a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x) = \\cfrac{20-4x}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"126\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p><u style=\"text-decoration-color:#FF9B28;\"><strong><span style=\"color:#1976d2;\">\u7b2c\u4e09\u6b65\uff1a<\/span><\/strong>\u627e\u5230\u5173\u952e\u70b9\u3002<\/u><\/p>\n<p>\u4e3a\u4e86\u627e\u5230\u51fd\u6570\u7684\u4e34\u754c\u70b9\uff0c\u6211\u4eec\u9700\u8981\u5c06\u5bfc\u6570\u8bbe\u7f6e\u4e3a\u96f6\u5e76\u6c42\u89e3\u6240\u5f97\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91e81f70cf7bd6388f6511629d203f7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5753c4fdb7aaae61182eac6fd15e52d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{20-4x}{4} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"91\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> 4 \u6574\u9664\u5de6\u4fa7\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e58\u4ee5\u6574\u4e2a\u53f3\u4fa7\u6765\u4e58\u4ee5\u5b83\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23e63171262e022c8a63e717b31ed0b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"20-4x=0 \\cdot 4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"113\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e9b9b9a13bafb9de785e9cf5b3e86ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"20-4x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"91\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e71409a99fca0883bc173a6df1b8c3af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-4x=-20\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"87\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-66b399752305ae60043d99032ba112d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-20}{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p><u style=\"text-decoration-color:#FF9B28;\"><span style=\"color:#1976d2;\"><strong>\u6b65\u9aa44\uff1a<\/strong><\/span>\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u5e76\u786e\u5b9a\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002<\/u><\/p>\n<p>\u4e3a\u4e86\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\uff0c\u6211\u4eec\u8868\u793a\u5728\u53f3\u4fa7\u627e\u5230\u7684\u4e34\u754c\u70b9\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-5.webp\" alt=\"\" class=\"wp-image-2466\" width=\"227\" height=\"88\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u786e\u5b9a\u51fd\u6570\u662f\u9012\u589e\u8fd8\u662f\u9012\u51cf\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u4e2d\u53d6\u4e00\u4e2a\u70b9\uff08\u800c\u4e0d\u662f\u4e34\u754c\u70b9\uff09\u5e76\u67e5\u770b\u5bfc\u6570\u5728\u8be5\u70b9\u7684\u7b26\u53f7\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00979b72662361213ec4611a28e935a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x) = \\cfrac{20-4x}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"126\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9c9fbc0304871964748873af9e9918c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(0) = \\cfrac{20-4\\cdot0}{4} = \\cfrac{20}{4} = 5  \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"264\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05c98faeaeb88c5826a71a45b3e9c88a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(6) = \\cfrac{20-4\\cdot6}{4} = \\cfrac{20-24}{4} = \\cfrac{-4}{4} = -1   \\  \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"373\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-5-positif-negatif.webp\" alt=\"\" class=\"wp-image-2467\" width=\"227\" height=\"160\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u5982\u679c\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u589e\uff0c\u5982\u679c\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u51cf\u3002\u56e0\u6b64\uff0c\u51fd\u6570\u589e\u51cf\u7684\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-188a50f6279237f5c478c7116a509d49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty, 5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-743f877080ce04389168296915ca6795_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(5,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5f53 x=5 \u65f6\uff0c\u51fd\u6570\u4ece\u589e\u52a0\u53d8\u4e3a\u51cf\u5c11\uff0c\u56e0\u6b64<strong>x=5 \u662f\u8981\u4f18\u5316\u7684\u51fd\u6570\u7684\u76f8\u5bf9\u6700\u5927\u503c<\/strong><strong>\u3002<\/strong><\/p>\n<p>\u56e0\u6b64\uff0cx=5\u662f\u4e09\u89d2\u5f62\u9762\u79ef\u6700\u5927\u7684\u5206\u652f\u7684\u503c\u3002\u7b80\u5355\u8ba1\u7b97\u53e6\u4e00\u6761\u817f\u7684\u4ef7\u503c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d396031e1a0eb65570a9f95d6701f9c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 10 -x \\ \\xrightarrow{x \\ = \\ 5} \\ y = 10-5= \\bm{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"265\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u603b\u4e4b\uff0c\u4f7f\u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef\u6700\u5927\u5316\u7684\u503c\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-85b25208de94c730a3de04d6d428dc59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=5} \\ \\mathbf{cm}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"75\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e7e41736bd949777d18ec2a79b0beb93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=5} \\ \\mathbf{cm}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"problemas-de-optimizacion-resueltos\"><\/span>\u4f18\u5316\u95ee\u9898\u5df2\u89e3\u51b3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u95ee\u98981<\/h3>\n<p>\u8be5\u836f\u662f\u7ed9\u75c5\u4eba\u7684\uff0c\u5e76\u4e14<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u51e0\u4e2a\u5c0f\u65f6\u540e\uff0c\u6d3b\u6027\u6210\u5206\u7684\u8840\u6db2\u6d53\u5ea6\u7531\u51fd\u6570\u7ed9\u51fa<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57f138f86e1400954205e4b91ed3103c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c(t) = te^{\u2212t\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u6beb\u514b\u6bcf\u6beb\u5347\u3002\u786e\u5b9a\u6700\u5927\u503c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4be04707471a329c8bde249ab6cf526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c(t)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5e76\u6307\u793a\u4f55\u65f6\u8fbe\u5230\u6240\u8ff0\u503c\u3002 <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa41\uff1a\u8bbe\u7f6e\u8981\u4f18\u5316\u7684\u529f\u80fd\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u4ed6\u4eec\u5df2\u7ecf\u7ed9\u4e86\u6211\u4eec\u5efa\u8bae\u7684\u51fd\u6570\uff0c\u5373<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02fb8044e28a7e9ba53c1eb64bfec693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle c(t) = t e^{-t\/2} .\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"100\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5f85\u4f18\u5316\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u8be5\u51fd\u6570\u7531 2 \u4e2a\u51fd\u6570\u7684\u4e58\u79ef\u7ec4\u6210\u3002\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u4e58\u79ef\u5bfc\u6570\u7684\u89c4\u5219\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1975d832fe40c4c12a2a4986244e3c24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle c'(t)=1 \\cdot e^{-t\/2} + t \\cdot e^{-t\/2} \\cdot \\left( \\frac{-t}{2} \\right)'= e^{-t\/2} + t e^{-t\/2} \\cdot  \\frac{-1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"430\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d730042a2ff5df46d19bce35fe24392_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c'(t)=e^{-t\/2} + \\cfrac{-1}{2}t  e^{-t\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"193\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u7b2c\u4e09\u6b65\uff1a\u627e\u5230\u5173\u952e\u70b9\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u627e\u5230\u51fd\u6570\u7684\u4e34\u754c\u70b9\uff0c\u6211\u4eec\u6c42\u89e3<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-626f673c4823e1bd527925bfe91d558f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c'(t)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64818981c87104d6e0b400434ce53533_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c'(t)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d9ebad9fa6bc78dc99b358f4786999f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle e^{-t\/2} + \\frac{-1}{2}t  e^{-t\/2}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"164\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u53d6\u516c\u56e0\u6570\u6765\u6c42\u89e3\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-410004b26bf5de6dc03c12491bee91b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle e^{-t\/2} \\left(1 - \\frac{1}{2}t \\right) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"150\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u4e58\u6cd5\u7b49\u4e8e 0\uff0c\u4e58\u6cd5\u7684\u4e24\u4e2a\u5143\u7d20\u4e4b\u4e00\u5fc5\u987b\u4e3a\u96f6\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u6bcf\u4e2a\u56e0\u5b50\u8bbe\u7f6e\u4e3a0\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8390139724dbc4ad014db2a76e508290_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle e^{-t\/2}\\cdot \\left(1 - \\frac{1}{2}t \\right) = 0 \\longrightarrow \\begin{cases} e^{-t\/2}=0 \\ \\bm{\\times} \\\\[2ex]\\displaystyle 1 - \\frac{1}{2}t=0 \\ \\longrightarrow \\ 1= \\frac{1}{2}t \\ \\longrightarrow \\ \\bm{2=t} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"486\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u4e2a\u6570\u4e0e\u53e6\u4e00\u4e2a\u6570\u76f8\u4e58\u6c38\u8fdc\u4e0d\u4f1a\u5f97\u5230 0\uff0c\u56e0\u6b64\uff0c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10b6a1e4b24bf63d08aeff4da0374d25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e^{-t\/2}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6ca1\u6709\u89e3\u51b3\u529e\u6cd5\u3002<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa44\uff1a\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u5e76\u786e\u5b9a\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\uff0c\u6211\u4eec\u8868\u793a\u5728\u53f3\u4fa7\u627e\u5230\u7684\u4e34\u754c\u70b9\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-2.webp\" alt=\"\" class=\"wp-image-2469\" width=\"204\" height=\"79\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u786e\u5b9a\u51fd\u6570\u662f\u9012\u589e\u8fd8\u662f\u9012\u51cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u53d6\u4e00\u4e2a\u70b9\uff08\u4e0d\u662f\u4e34\u754c\u70b9\uff09\uff0c\u5e76\u67e5\u770b\u6b64\u65f6\u5bfc\u6570\u7684\u7b26\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-904d140578309f45e9c53d2a9a35e32d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle c'(0)=e^{-0\/2} + \\frac{-1}{2}\\cdot 0 \\cdot e^{-0\/2} = e^0 +\\frac{-1}{2}\\cdot 0 \\cdot e^{0} = 1 + 0 = 1 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"508\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ada4b79153afee560564a81df8d0c46f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle c'(3)=e^{-3\/2} + \\frac{-1}{2}(3)e^{-3\/2} = 0,22-0,33 = -0,11 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"449\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-deux-positif-negatif.webp\" alt=\"\" class=\"wp-image-2472\" width=\"202\" height=\"143\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u51fd\u6570\u589e\u5927\uff0c\u53cd\u4e4b\uff0c\u5982\u679c\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u51fd\u6570\u51cf\u5c0f\u3002\u56e0\u6b64\u5f85\u4f18\u5316\u51fd\u6570\u7684\u589e\u957f\u548c\u4e0b\u964d\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3868632c123ece40100b3a40c266cc25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c9901d11cc4672cab7e1e2a6de08ce4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u51fd\u6570\u5728 t=2 \u65f6\u4ece\u589e\u52a0\u53d8\u4e3a\u51cf\u5c11\uff0c\u56e0\u6b64<strong>t=2 \u662f\u8be5\u51fd\u6570\u7684\u6700\u5927\u503c<\/strong>\u3002\u56e0\u6b64\u5c06\u5728<strong>t=2\u5c0f\u65f6\u5185\u8fbe\u5230\u6700\u5927\u6d53\u5ea6\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u5c06\u6700\u5927\u503c\u51fa\u73b0\u7684\u503c\u4ee3\u5165\u539f\u51fd\u6570\uff0c\u6c42\u5f97\u6700\u5927\u6d53\u5ea6\u503c\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd8123e6fd3fe714d1784775375011f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c(2) = 2 \\cdot e^{-2\/2} = 2\\cdot e^{-1} = 2 \\cdot 0,37 = \\bm{0,74} \\ \\mathbf{mg\/ml}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"391\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u95ee\u98982<\/h3>\n<p>\u4e00\u5bb6\u5546\u5e97\u5e0c\u671b\u4ee5\u6bcf\u8f86 1,000 \u6b27\u5143\u7684\u4ef7\u683c\u51fa\u552e 40 \u8f86\u7535\u52a8\u6ed1\u677f\u8f66\u3002\u4f46\u6839\u636e\u5e02\u573a\u7814\u7a76\uff0c\u6ed1\u677f\u8f66\u4ef7\u683c\u6bcf\u964d\u4f4e 50 \u6b27\u5143\uff0c\u6700\u7545\u9500\u7684\u524d 10 \u540d\u6ed1\u677f\u8f66\u7684\u9500\u91cf\u5c31\u4f1a\u589e\u52a0\u3002<\/p>\n<p>\u9996\u5148\u6839\u636e\u8e0f\u677f\u8f66\u539f\u4ef7 1,000 \u7f8e\u5143\u964d\u4f4e 50 \u7f8e\u5143\u7684\u6b21\u6570\u7f16\u5199\u5546\u5e97\u7684\u6536\u5165\u51fd\u6570\u3002\u63a5\u4e0b\u6765\uff0c\u786e\u5b9a\u83b7\u5f97\u6700\u5927\u5229\u6da6\u7684\u6ed1\u677f\u8f66\u4ef7\u683c\u4ee5\u53ca\u5728\u8be5\u4ef7\u683c\u4e0b\u83b7\u5f97\u7684\u6536\u5165\u3002 <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa41\uff1a\u8bbe\u7f6e\u8981\u4f18\u5316\u7684\u529f\u80fd\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u95ee\u9898\u9648\u8ff0\u7ed9\u4e86\u6211\u4eec\u4e00\u4e2a\u7ebf\u7d22\uff0c\u56e0\u4e3a\u5b83\u544a\u8bc9\u6211\u4eec\u8be5\u51fd\u6570\u5fc5\u987b\u53d6\u51b3\u4e8e\u521d\u59cb\u4ef7\u683c\u51cf\u5c11 50 \u7f8e\u5143\u7684\u6b21\u6570\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u4ef7\u683c\u964d\u4f4e 50 \u6b27\u5143\u7684\u6b21\u6570\u79f0\u4e3a x\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d0357e75c58ab161e387dae18d3a6f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= \\text{N\\'umero de veces que se rebaja el precio 50}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"368\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6b27\u5143<\/p>\n<p class=\"has-text-align-left\">\u6536\u5165\u51fd\u6570\u5c06\u662f\u552e\u51fa\u7684\u8e0f\u677f\u8f66\u6570\u91cf\u4e58\u4ee5\u6bcf\u8f86\u8e0f\u677f\u8f66\u7684\u4ef7\u683c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f04d6d19de5d7a7ad8dceadfbbdbdbe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= \\text{N\\'umero patintetes vendidos} \\cdot \\text{Precio de cada patinete}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"470\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u552e\u51fa\u7684\u8e0f\u677f\u8f66\u6570\u91cf\u5c06\u4e3a 40 \u8f86\uff0c\u6bcf\u964d\u4ef7 50 \u6b27\u5143\u5373\u53ef\u552e\u51fa 10 \u8f86\u8e0f\u677f\u8f66\u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88b7464372c9683d065acbdbe2598cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{N\\'umero patintetes vendidos} = 40 + 10x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"308\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6bcf\u8f86\u8e0f\u677f\u8f66\u7684\u8d77\u59cb\u4ef7\u683c\u4e3a 1000 \u6b27\u5143\uff0c\u6bcf\u6b21\u964d\u4ef7\u5c06\u964d\u4f4e 50 \u6b27\u5143\u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c22a7a64d350ea748ad2b4b3decd217_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Precio de cada patinete} = 1000 -50x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"291\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4f18\u5316\u95ee\u9898\u7684\u51fd\u6570\u662f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f04d6d19de5d7a7ad8dceadfbbdbdbe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= \\text{N\\'umero patintetes vendidos} \\cdot \\text{Precio de cada patinete}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"470\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2cbffd131757d106f869b562d4e35c4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= (40 + 10x) \\cdot (1000-50x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"249\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ae987678d7542e5d127fc02f8bf4daf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= 40000-2000x+10000x-500x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-902cc0a5c209ed48e3d93432b5550b1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= -500x^2+8000x+40000\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"249\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5f85\u4f18\u5316\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4f5c\u4e3a\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u5bfc\u6570\u66f4\u5bb9\u6613\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acb8d705be4d3a30be83d2800f4d2403_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= -500x^2+8000x+40000\\ \\longrightarrow \\ I'(x)= -1000x+8000\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"477\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u7b2c\u4e09\u6b65\uff1a\u627e\u51fa\u51fd\u6570\u7684\u4e34\u754c\u70b9\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u627e\u5230\u51fd\u6570\u7684\u4e34\u754c\u70b9\uff0c\u6211\u4eec\u6c42\u89e3<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b55b4fb6ca5af90f829cb082893a5519_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8b48142b0c92fea1f9dd87af211ada6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a0d58fd339d02e3f71b7fe031726cad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1000x+8000=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"148\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a03bae4e019041d174c51fced30954ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1000x=-8000\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"132\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e67f8bf53c9c10c3384f729890f57b4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-8000}{-1000} = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"125\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa44\uff1a\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u5e76\u786e\u5b9a\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u51fa\u7684\u4e34\u754c\u70b9\u8868\u793a\u5728\u6570\u8f74\u4e0a\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-8.webp\" alt=\"\" class=\"wp-image-2481\" width=\"234\" height=\"91\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u786e\u5b9a\u51fd\u6570\u662f\u9012\u589e\u8fd8\u662f\u9012\u51cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u53d6\u4e00\u4e2a\u70b9\uff08\u4e0d\u662f\u4e34\u754c\u70b9\uff09\uff0c\u5e76\u67e5\u770b\u6b64\u65f6\u5bfc\u6570\u7684\u7b26\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3cf47c71ae832d734c6e5f525efa05b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I'(0)= -1000\\cdot 0+8000=8000 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"300\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9df9f5fdff3d4ba6dcd7f17c68b16c2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I'(10)= -1000\\cdot 10+8000=-2000 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"331\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-8-positif-negatif.webp\" alt=\"\" class=\"wp-image-2482\" width=\"239\" height=\"169\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u589e\uff0c\u5982\u679c\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u51cf\u3002\u56e0\u6b64\uff0c\u589e\u957f\u533a\u95f4\u548c\u4e0b\u964d\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d85d36c78a812c7c5a8f127bb5145c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,8)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ba6980946255650ee8fe4dbc4c87c681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(8,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u51fd\u6570\u5728 x=8 \u5904\u4ece\u589e\u52a0\u53d8\u4e3a\u51cf\u5c11\uff0c\u56e0\u6b64<strong>x=8 \u662f\u8be5\u51fd\u6570\u7684\u6700\u5927\u503c<\/strong>\u3002\u56e0\u6b64\uff0c<strong>\u51cf\u5c11 50 \u6b27\u5143\u7684 8 \u500d\u5373\u53ef\u83b7\u5f97\u6700\u5927\u6536\u5165\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u6700\u5927\u6536\u5165\u51fa\u73b0\u7684\u503c\u4ee3\u5165\u539f\u51fd\u6570\uff0c\u6c42\u51fa\u6700\u5927\u6536\u5165\u7684\u503c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-902cc0a5c209ed48e3d93432b5550b1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(x)= -500x^2+8000x+40000\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"249\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fce0d14898ab44824c50e758de24099d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(8)= -500\\cdot 8^2+8000\\cdot 8+40000 = \\bm{72000}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"339\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>\u6b27\u5143<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4eab\u53d7 50 \u6b27\u5143\u6298\u6263 8 \u6b21\u540e\uff0c\u6bcf\u8f86\u8e0f\u677f\u8f66\u7684\u4ef7\u683c\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c22a7a64d350ea748ad2b4b3decd217_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Precio de cada patinete} = 1000 -50x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"291\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a4646c3d785d36e70ba549b9672b697c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Precio de cada patinete} = 1000 -50\\cdot 8=\\bm{600}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"353\" style=\"vertical-align: -4px;\"><\/p>\n<p><strong>\u6b27\u5143<\/strong><\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u95ee\u98983<\/h3>\n<p>\u516c\u53f8\u7684\u6210\u672c\u51fd\u6570\uff08\u4ee5\u5343\u6b27\u5143\u4e3a\u5355\u4f4d\uff09\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u786e\u5b9a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c84c0900acd506ad979886e5b5f10ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=40-6x+x^2, \\quad x \\ge  0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"224\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4ee3\u8868\u7ed9\u5b9a\u4ea7\u54c1\u751f\u4ea7\u7684\u6570\u5343\u4e2a\u5355\u4f4d\u3002<\/p>\n<p>\u786e\u5b9a\u5fc5\u987b\u751f\u4ea7\u591a\u5c11\u624d\u80fd\u4f7f\u6210\u672c\u6700\u5c0f\uff0c\u8be5\u6210\u672c\u662f\u591a\u5c11\uff0c\u4ee5\u53ca\u5982\u679c\u4e0d\u751f\u4ea7\u8fd9\u4e9b\u7269\u54c1\uff0c\u6210\u672c\u662f\u591a\u5c11\u3002 <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa41\uff1a\u8bbe\u7f6e\u8981\u4f18\u5316\u7684\u529f\u80fd\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u95ee\u9898\u9648\u8ff0\u5df2\u7ecf\u7ed9\u6211\u4eec\u63d0\u4f9b\u4e86\u9700\u8981\u4f18\u5316\u7684\u51fd\u6570\uff0c\u5373<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6dc6eb92c2776f8026c348e7e5824d09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=40-6x+x^2 .\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"160\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5f85\u4f18\u5316\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5056826599d14c0ff8aa3ec134a68b0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=40-6x+x^2 \\ \\longrightarrow \\ f'(x)=-6+2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"332\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u7b2c\u4e09\u6b65\uff1a\u627e\u5230\u5173\u952e\u70b9\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u627e\u5230\u51fd\u6570\u7684\u4e34\u754c\u70b9\uff0c\u6211\u4eec\u6c42\u89e3<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-58dcd049349f740f082d583dfd9e364c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ecec21f50b0875af5ebb5c55ef5e2502_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-6+2x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"95\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d47687d0a8cb82ab26be7eadf0d7f3c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x=6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f1ffe509b34b0d560397fbc1859cb64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{6}{2} = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"77\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa44\uff1a\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u5e76\u786e\u5b9a\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8868\u793a\u5728\u53f3\u4fa7\u627e\u5230\u7684\u4e34\u754c\u70b9\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-3.webp\" alt=\"\" class=\"wp-image-2485\" width=\"231\" height=\"90\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u786e\u5b9a\u51fd\u6570\u662f\u9012\u589e\u8fd8\u662f\u9012\u51cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u53d6\u4e00\u4e2a\u70b9\uff08\u4e0d\u662f\u4e34\u754c\u70b9\uff09\uff0c\u5e76\u67e5\u770b\u6b64\u65f6\u5bfc\u6570\u7684\u7b26\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2647164feab3d1bdc3e7cdb14c123294_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(0)=-6+2\\cdot 0=-6\\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"235\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fe3f1add3273a0ba4d0418a3b9788a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(4)=-6+2\\cdot 4=-6+8=2\\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"298\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-3-negatif-positif.webp\" alt=\"\" class=\"wp-image-2486\" width=\"231\" height=\"163\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u5bfc\u6570\u5927\u4e8e\u96f6\uff0c\u5219\u51fd\u6570\u5728\u6b64\u533a\u95f4\u5185\u589e\u52a0\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u5bfc\u6570\u5c0f\u4e8e\u96f6\uff0c\u5219\u51fd\u6570\u5728\u6b64\u533a\u95f4\u5185\u51cf\u5c0f\u3002\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u589e\u52a0\u548c\u51cf\u5c11\u7684\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbc0e31e2b07080a4f83c2a34053c0f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(3,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a890e45091b2c4c9115051361c0a1a2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728 x=3 \u5904\uff0c\u51fd\u6570\u4ece\u9012\u51cf\u53d8\u4e3a\u9012\u589e\uff0c\u56e0\u6b64<strong>x=3 \u662f\u51fd\u6570\u7684\u6700\u5c0f\u503c<\/strong>\u3002\u56e0\u6b64\uff0c\u751f\u4ea7<strong>3000\u53f0\u5373\u53ef\u5b9e\u73b0\u6700\u4f4e\u6210\u672c\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u8fbe\u5230\u6700\u5c0f\u6210\u672c\u7684\u503c\u4ee3\u5165\u539f\u59cb\u51fd\u6570\u6765\u627e\u5230\u6700\u5c0f\u6210\u672c\u503c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a1c84d3c81fd4c7ebbecc922cc2288e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3)=40-6\\cdot 3+3^2=\\bm{31}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"206\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u6570\u767e\u4e07\u6b27\u5143\u3002<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u4ed6\u4eec\u95ee\u6211\u4eec\uff0c\u5982\u679c\u4ec0\u4e48\u90fd\u4e0d\u751f\u4ea7\uff0c\u6210\u672c\u662f\u591a\u5c11\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4ec0\u4e48\u65f6\u5019<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa5140cb12e100167e56a99c53750148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u56e0\u6b64\u9700\u8981\u8ba1\u7b97<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f92d7beea0ed3a053927c2d429d3450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7051466b3981f72509f3e5e2aa1d2f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=40-6\\cdot 0+0^2=   \\bm{40}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u6570\u767e\u4e07\u6b27\u5143\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u95ee\u98984<\/h3>\n<p>\u6211\u4eec\u60f3\u8981\u5efa\u9020\u4e00\u4e2a\u77e9\u5f62\u6728\u6846\u67b6\uff0c\u5176\u9762\u79ef\u4e3a 2 m <sup>2<\/sup> \u3002\u6211\u4eec\u77e5\u9053\uff0c\u6c34\u5e73\u8fb9\u7684\u6728\u6750\u4ef7\u683c\u4e3a 7.5 \u6b27\u5143\/\u7c73\uff0c\u5782\u76f4\u8fb9\u7684\u6728\u6750\u4ef7\u683c\u4e3a 12.5 \u6b27\u5143\/\u7c73\u3002\u786e\u5b9a\u77e9\u5f62\u5fc5\u987b\u5177\u6709\u7684\u5c3a\u5bf8\uff0c\u4ee5\u4f7f\u6846\u67b6\u7684\u603b\u6210\u672c\u5c3d\u53ef\u80fd\u6700\u5c0f\uff0c\u5e76\u4e14\u6240\u8ff0\u6210\u672c\u4e5f\u6700\u5c0f\u3002 <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa41\uff1a\u8bbe\u7f6e\u8981\u4f18\u5316\u7684\u529f\u80fd\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u6c34\u5e73\u8fb9\u79f0\u4e3a<em>x<\/em> \uff0c\u5c06\u5782\u76f4\u8fb9\u79f0\u4e3a<em>y<\/em> \uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/rectangle-fonction-optimisation-problemes.webp\" alt=\"\u77e9\u5f62\u51fd\u6570\u4f18\u5316\u95ee\u9898\" class=\"wp-image-2490\" width=\"166\" height=\"188\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u8d2d\u4e70\u6c34\u5e73\u8fb9\u7684\u8d39\u7528\u4e3a 7.5 \u6b27\u5143\uff0c\u8d2d\u4e70\u5782\u76f4\u8fb9\u7684\u8d39\u7528\u4e3a 12.5 \u6b27\u5143\u3002\u6b64\u5916\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u6846\u67b6\uff0c\u6211\u4eec\u9700\u8981\u4e24\u4e2a\u6c34\u5e73\u8fb9\u548c\u4e24\u4e2a\u5782\u76f4\u8fb9\u3002\u56e0\u6b64\uff0c\u6846\u67b6\u7684\u6210\u672c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u51fd\u6570\u786e\u5b9a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8485280ab046816dfbd587b192901fb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(x,y)= 7,5\\cdot 2x+12,5 \\cdot 2y = 15x +25y\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"323\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5df2\u7ecf\u6709\u4e86\u4f18\u5316\u7684\u529f\u80fd\u3002\u4f46\u5f53\u5b83\u53ea\u80fd\u53d6\u51b3\u4e8e\u4e00\u4e2a\u53d8\u91cf\u65f6\uff0c\u5b83\u53d6\u51b3\u4e8e\u4e24\u4e2a\u53d8\u91cf\u3002\u7136\u800c\uff0c\u58f0\u660e\u544a\u8bc9\u6211\u4eec\u6846\u67b6\u7684\u8868\u9762\u79ef\u5fc5\u987b\u4e3a2 m <sup>2<\/sup> \u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-13ea4da7e9b4674fdd1a733e0e3cd26e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x \\cdot y = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"64\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5220\u9664\u53d8\u91cf<em>y<\/em> \uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e00a5c6da8de49964d27f2941dac8a4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =\\cfrac{2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"46\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u66ff\u6362\u5728\u8981\u4f18\u5316\u7684\u51fd\u6570\u4e2d\u627e\u5230\u7684\u8868\u8fbe\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2cb9add65869ac746532ac4bf1537eb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(x,y)= 15x +25y\\ \\xrightarrow{y \\ = \\ \\frac{2}{x} } \\ C(x)= 15x+25\\left(\\cfrac{2}{x} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"396\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e232dbf6025d3b8d6593e4157cd09bff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(x)= 15x+\\cfrac{50}{x} =15x +50x^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5f85\u4f18\u5316\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ef3647de078c1f760dc37a5d3d6b68e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(x)=15x +50x^{-1} \\ \\longrightarrow \\ C'(x)=15 -50x^{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"359\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u7b2c\u4e09\u6b65\uff1a\u627e\u5230\u5173\u952e\u70b9\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u627e\u5230\u51fd\u6570\u7684\u4e34\u754c\u70b9\uff0c\u6211\u4eec\u6c42\u89e3<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97f234a562c87b78e257fc7953dee7ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8732228827d41a41af6935b1f0bdc0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdaf71028a32e2818a7ec3376338df75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15 -50x^{-2}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"117\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8bf1bee39e8e6e8f54b838f7dc8810d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15 =50x^{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"86\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4f9337813bfb8c7bf0d09f9889514c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15=\\cfrac{50}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"60\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0aea588515cc1c895b2ca5030cd55ffc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{15}{1}=\\cfrac{50}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"61\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6a2a\u5411\u76f8\u4e58\u6765\u6c42\u89e3\u5206\u6570\u65b9\u7a0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99a602636bc09eb630e637ec6454c8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15 \\cdot x^2 = 50 \\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"110\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dcdd7918a1af31e63925cb694da7d6be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2 = \\cfrac{50}{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"61\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e9090b3956470b16769ec2ae441f2d30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2 = 3,33\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-92abf359db44a399822919b1bb62e7cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^2} = \\sqrt{3,33}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"105\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b87ffa5999c0bbea78cc07d6a412460a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = 1,83\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"69\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa44\uff1a\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u5e76\u786e\u5b9a\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u627e\u5230\u7684\u4e34\u754c\u70b9\u8868\u793a\u4e3a\u5728\u7ebf\u5206\u6790\u51fd\u6570\u7684\u5355\u8c03\u6027\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-183.webp\" alt=\"\" class=\"wp-image-2491\" width=\"206\" height=\"80\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u786e\u5b9a\u51fd\u6570\u662f\u9012\u589e\u8fd8\u662f\u9012\u51cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u53d6\u4e00\u4e2a\u70b9\uff08\u4e0d\u662f\u4e34\u754c\u70b9\uff09\uff0c\u5e76\u67e5\u770b\u6b64\u65f6\u5bfc\u6570\u7684\u7b26\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64f2221e9103ecdcb21609567e990135_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(1)=15 -50\\cdot 1^{-2} = 15-50 = -35 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"347\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad12501e06c6997d1555df684480d38b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2)=15 -50\\cdot 2^{-2} = 15-12,5 = 2,5 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"358\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-183-negatif-positif.webp\" alt=\"\" class=\"wp-image-2493\" width=\"206\" height=\"146\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u589e\uff0c\u5982\u679c\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u51cf\u3002\u56e0\u6b64\uff0c\u589e\u957f\u533a\u95f4\u548c\u4e0b\u964d\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d8e4f82a46ac576b10134beda86f0bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,83,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57f0911e594b424ad7908294a15f1b84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,1,83)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728 x=1.83 \u5904\uff0c\u51fd\u6570\u4ece\u9012\u51cf\u53d8\u4e3a\u9012\u589e\uff0c\u56e0\u6b64<strong>x=1.83 \u662f\u51fd\u6570\u7684\u6700\u5c0f\u503c<\/strong>\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0cx=1.83 \u662f\u4ee3\u8868\u6700\u5c0f\u6210\u672c\u7684\u6c34\u5e73\u8fb9\u7684\u503c\u3002\u73b0\u5728\u6211\u4eec\u6765\u8ba1\u7b97\u5782\u76f4\u8fb9\u7684\u503c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-325134d449963e4d814cdd19a87bdfd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =\\cfrac{2}{x} \\ \\longrightarrow \\ y =\\cfrac{2}{1,83} = \\bm{1,09}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"223\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6784\u6210\u6700\u5c0f\u6846\u67b6\u6210\u672c\u7684\u503c\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\">\u6c34\u5e73\u8fb9<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c8b9148690c3a5b5e441df6c02e23e85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"= x = \\bm{1,83} \\ \\mathbf{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"110\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\u5782\u76f4\u8fb9<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ad15cb0e6023282190abbb21c5f8a47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"= y = \\bm{1,09} \\ \\mathbf{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u800c\u8fd9\u4e9b\u503c\u8fbe\u5230\u7684\u6700\u5c0f\u6210\u672c\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bef42a21eacaeb4cd25b5e43c15e268b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C= 15\\cdot 1,83+25\\cdot 1,09=\\bm{54,70}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"256\" style=\"vertical-align: -4px;\"><\/p>\n<p><strong>\u6b27\u5143<\/strong><\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u95ee\u98985<\/h3>\n<p>\u5927\u6559\u5802\u7684\u95e8\u662f\u7531\u4e24\u6839\u67f1\u5b50\u652f\u6491\u7684\u534a\u5706\u5468\u62f1\u95e8\u7ec4\u6210\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/problemes-d-optimisation-de-la-geometrie.webp\" alt=\"\u51e0\u4f55\u4f18\u5316\u95ee\u9898\" class=\"wp-image-2500\" width=\"182\" height=\"268\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u5982\u679c\u95e8\u7684\u5468\u957f\u4e3a 20 m\uff0c\u8bf7\u786e\u5b9a\u5c3a\u5bf8<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u8fd9\u6700\u5927\u5316\u4e86\u6574\u4e2a\u95e8\u7684\u8868\u9762\u79ef\u3002 <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa41\uff1a\u8bbe\u7f6e\u8981\u4f18\u5316\u7684\u529f\u80fd\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u5706\u7684\u9762\u79ef\u7528\u516c\u5f0f\u8ba1\u7b97<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1ab0b6b8d454bae5631e7a82caed58d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi r^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6240\u4ee5\u6574\u4e2a\u95e8\u7684\u9762\u79ef\u5c06\u662f\u77e9\u5f62\u7684\u9762\u79ef\u52a0\u4e0a\u5706\u5468\u9762\u79ef\u7684\u4e00\u534a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-95c1f9b6152c4cbc623aeb8a0a5757b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x\\cdot y + \\cfrac{1}{2} \\left[ \\pi r ^2 \\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-baa2e14b061cf14a657782db8fe91b92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x y + \\cfrac{1}{2} \\left[ \\pi \\left(\\cfrac{x}{2}\\right)^2 \\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"212\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9196d8284edebe6450d49aa5a0b6a3e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x y + \\cfrac{1}{2} \\left[ \\pi \\cdot \\cfrac{x^2}{4} \\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"193\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b25e1d2c661585be998d1596d6650c01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x y +\\cfrac{1}{2} \\left[  \\cfrac{\\pi \\cdot x^2}{4} \\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"193\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64a0c7fa480320a1b564fec5f9ff8265_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= xy +\\cfrac{\\pi x^2}{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"150\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5df2\u7ecf\u6709\u4e86\u4f18\u5316\u7684\u529f\u80fd\u3002\u4f46\u5f53\u5b83\u53ea\u80fd\u53d6\u51b3\u4e8e\u4e00\u4e2a\u53d8\u91cf\u65f6\uff0c\u5b83\u53d6\u51b3\u4e8e\u4e24\u4e2a\u53d8\u91cf\u3002<\/p>\n<p class=\"has-text-align-left\">\u4e0d\u8fc7\uff0c\u53d1\u5e03\u7684\u6d88\u606f\u544a\u8bc9\u6211\u4eec\uff0c\u6574\u4e2a\u5927\u95e8\u7684\u5468\u957f\u4e3a20m\u3002\u5706\u7684\u5468\u957f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e815d233e188a7121eef89639e48fe75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\pi r.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u6574\u4e2a\u95e8\u7684\u5468\u957f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7709d0c72bf84a17ac83bc46f5cce002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P= x +2y +\\cfrac{1}{2} \\left[ 2 \\pi \\left( \\cfrac{x}{2}\\right) \\right] = x+2y + \\cfrac{2 \\pi x }{2 \\cdot 2} = x+2y + \\cfrac{ \\pi x }{2 }\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"452\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5468\u957f\u5fc5\u987b\u4e3a 20 m\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u8bbe\u7f6e\u4e3a\u7b49\u4e8e 20 \u6765\u67e5\u627e\u4e4b\u95f4\u7684\u5173\u7cfb<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a70e6a4387a816f153e8597195143f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-282aa8aebdd04ba4989ba7466fdd694d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+2y + \\cfrac{ \\pi x }{2 } = 20\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"136\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u6211\u4eec\u5c06\u6240\u6709\u9879\u4e58\u4ee5 2 \u4ee5\u6d88\u9664\u5206\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a185cfda7fb65f370636fa469b0de2c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot x+2\\cdot 2y + 2 \\cdot \\cfrac{ \\pi x }{2 } = 2 \\cdot 20\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"223\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d67cd2fbdde0f884603e75bf270cb52c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+4y +  \\pi x = 40\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"143\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6e05\u9664<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a70e6a4387a816f153e8597195143f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-740ff13a6824a3ee18cb1de0cbf52660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4y  = 40-2x- \\pi x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"143\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db16e16a94223af02d63ea70eae3db7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y   = \\cfrac{40-2x- \\pi x}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"136\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u66ff\u6362\u5728\u8981\u4f18\u5316\u7684\u51fd\u6570\u4e2d\u627e\u5230\u7684\u8868\u8fbe\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16c3b1d1a3ac443d4640ae2b72c164e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x,y)= x y +\\cfrac{\\pi x^2}{8}\\ \\xrightarrow{y \\ = \\ \\frac{40-2x- \\pi x}{4} }\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"262\" style=\"vertical-align: -12px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f463f9095e8028624678c06a08696a96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x)= x \\cdot \\cfrac{40-2x- \\pi x}{4}+\\cfrac{\\pi x^2}{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"239\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-095586f92b592c3c9c50750f8a6eb7d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x)= \\cfrac{40x-2x^2-\\pi x^2}{4}+\\cfrac{\\pi x^2}{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"242\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5f85\u4f18\u5316\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42ce3330af662099ad431ee1187d26f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x)=\\cfrac{(40-4x-2\\pi x)\\cdot 4 +(40x-2x^2- \\pi x^2)\\cdot 0 }{4^2} +\\cfrac{2\\pi x \\cdot 8 + \\pi x^2 \\cdot 0}{8^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"544\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a75cddf1efd4f17b6a3211093f2e0b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x)=\\cfrac{160-16x-8\\pi x }{16} +\\cfrac{16\\pi x}{64}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"257\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u7b2c\u4e09\u6b65\uff1a\u627e\u5230\u5173\u952e\u70b9\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u627e\u5230\u51fd\u6570\u7684\u4e34\u754c\u70b9\uff0c\u6211\u4eec\u6c42\u89e3<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8f5a921f7e1978b553d11a76e0962c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-424f3d5d91120e872bebd055792d71a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89a04d2a2a532f36f15042d2d2c79d41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{160-16x-8\\pi x }{16} +\\cfrac{16\\pi x}{64} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"222\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8fd9\u662f\u4e00\u4e2a\u5e26\u6709\u5206\u6570\u7684\u65b9\u7a0b\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u6bcf\u4e00\u9879\u4e58\u4ee5\u5206\u6bcd\u7684 lcm \u4ee5\u6d88\u9664\u5206\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-87d60f06d42276c79b3a4f33b00fdb7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"64 \\cdot \\cfrac{160-16x-8\\pi x }{16} +64 \\cdot \\cfrac{16\\pi x}{64} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"285\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2a7b3bbdad1ea1bf9f12861b1dbdf0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot ( 160-16x-8\\pi x) +1\\cdot 16\\pi x= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61a4622d4b65310580e066941ae13fac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"640-64x -32 \\pi x +16\\pi x= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"229\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-94c6efd66ea5f2f1c68ab09d59fb5432_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-64x -32 \\pi x +16\\pi x= -640\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"226\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bdaf73c6d74c3d4f605b5aea3cdeb1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-64x -16 \\pi x = -640\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4bfe710d37882f664daed4de23f2eb7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-64 -16 \\pi) x = -640\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b551560fd86665e639dbc88aeb88a2bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-640}{-64 -16 \\pi}  = 5,6\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"167\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa44\uff1a\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u5e76\u786e\u5b9a\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\uff0c\u6211\u4eec\u8868\u793a\u5728\u53f3\u4fa7\u627e\u5230\u7684\u4e34\u754c\u70b9\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-56.webp\" alt=\"\" class=\"wp-image-2501\" width=\"214\" height=\"83\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u786e\u5b9a\u51fd\u6570\u662f\u9012\u589e\u8fd8\u662f\u9012\u51cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u53d6\u4e00\u4e2a\u70b9\uff08\u4e0d\u662f\u4e34\u754c\u70b9\uff09\uff0c\u5e76\u67e5\u770b\u6b64\u65f6\u5bfc\u6570\u7684\u7b26\u53f7\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8b0c6b03e591be56505c8853595dd0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(0)=\\cfrac{160-16\\cdot 0-8\\pi \\cdot 0 }{16} +\\cfrac{16\\pi \\cdot 0}{64} = 10 +0 = 10 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"456\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91c7e9012e4937dad79ec792910df916_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A'(6)=\\cfrac{160-16\\cdot 6-8\\pi \\cdot 6 }{16} +\\cfrac{16\\pi \\cdot 6}{64} = -5,42 +4,71 = -0,71 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"543\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-56-positif-negatif.webp\" alt=\"\" class=\"wp-image-2503\" width=\"218\" height=\"155\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u589e\uff0c\u5982\u679c\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u51cf\u3002\u56e0\u6b64\uff0c\u589e\u957f\u533a\u95f4\u548c\u4e0b\u964d\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-375f15fd5182721ee68f606765b66e89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty , 5,6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce3629c3ea3fa84fd3413a15913976f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(5,6,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u51fd\u6570\u5728 x=5.6 \u5904\u4ece\u589e\u52a0\u53d8\u4e3a\u51cf\u5c11\uff0c\u56e0\u6b64<strong>x=5.6 \u662f\u8be5\u51fd\u6570\u7684\u6700\u5927\u503c<\/strong>\u3002<\/p>\n<p class=\"has-text-align-left\">\u7136\u800c\uff0c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0d40793b19725cb50b88536bdaf3239_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5,6\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"60\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u5f62\u6210\u6700\u5927\u8868\u9762\u7684\u503c\u3002\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u7684\u503c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a70e6a4387a816f153e8597195143f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-af3ff0bf06cb82b6661c9ead44cabaa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = \\cfrac{40-2\\cdot 5,6- \\pi \\cdot 5,6}{4} = 2,80\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"251\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u56e0\u6b64\uff0c\u6784\u6210\u6700\u5927\u8868\u9762\u79ef\u7684\u503c\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25cd4efdc51c2a6fb453056df61536fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x = 5,60} \\ \\mathbf{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b69c85499698e995f01f60b2b78ef20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y = 2,80} \\ \\mathbf{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u95ee\u98986<\/h3>\n<p>\u6211\u4eec\u8981\u5efa\u9020\u4e00\u4e2a\u9762\u79ef\u4e3a54 cm <sup>2<\/sup>\u7684\u5706\u67f1\u5f62\u6c34\u7bb1\u3002\u786e\u5b9a\u5706\u67f1\u4f53\u7684\u5e95\u9762\u534a\u5f84\u548c\u9ad8\u5ea6\uff0c\u4f7f\u4f53\u79ef\u6700\u5927\u3002 <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa41\uff1a\u8bbe\u7f6e\u8981\u4f18\u5316\u7684\u529f\u80fd\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u5706\u67f1\u4f53\u7684\u4f53\u79ef\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbe33001d54c8245539894746beb9eac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V= A_{base}\\cdot h\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"101\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5e95\u9762\u79ef\u662f\u5706\uff0c\u6240\u4ee5\u5b83\u7684\u516c\u5f0f\u662f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc935e01b9c94505406438dea94cf121_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_{\\text{base}}=\\pi r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u3002\u56e0\u6b64\uff0c\u5706\u67f1\u4f53\u7684\u4f53\u79ef\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df6ffff5ee54af4f7b10424871d1af92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V= \\pi r^2 \\cdot h\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"88\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5df2\u7ecf\u6709\u4e86\u4f18\u5316\u7684\u529f\u80fd\u3002\u4f46\u8fd9\u53d6\u51b3\u4e8e\u4e24\u4e2a\u53d8\u91cf\uff08<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff09\uff0c\u800c\u5b83\u53ea\u80fd\u4f9d\u8d56\u4e8e\u4e00\u4e2a\u3002\u7136\u800c\uff0c\u58f0\u660e\u544a\u8bc9\u6211\u4eec\uff0c\u5706\u67f1\u4f53\u7684\u9762\u79ef\u5fc5\u987b\u662f 54 cm <sup>2<\/sup> \uff0c\u6240\u4ee5\u6211\u4eec\u8981\u5229\u7528\u8fd9\u4e2a\u6761\u4ef6\u6765\u627e\u5230\u4e4b\u95f4\u7684\u5173\u7cfb<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f0bf134a8aafe0dfaa4d711f78b8b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u5706\u67f1\u4f53\u7684\u9762\u79ef\uff0c\u5fc5\u987b\u5c06\u5176\u4fa7\u9762\u79ef\u4e0e\u4e24\u4e2a\u5e95\u9762\u7684\u9762\u79ef\u76f8\u52a0\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/problemes-optimisation-des-fonctions-verins.webp\" alt=\"\u5706\u67f1\u51fd\u6570\u7684\u4f18\u5316\u95ee\u9898.png\" class=\"wp-image-2507\" width=\"557\" height=\"271\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-edd9578a95d32143e6eaf0830db3854b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_{cilindro} = A_{lateral}+2A_{base} = 2\\pi r h + 2\\pi r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"330\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5706\u67f1\u4f53\u7684\u9762\u79ef\u5fc5\u987b\u4e3a54 cm <sup>2<\/sup> \uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u8bbe\u7f6e\u4e3a\u7b49\u4e8e54\uff0c\u4ee5\u83b7\u5f97\u4e4b\u95f4\u7684\u5173\u7cfb<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6868abdfd034048aa59644d2ac62353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ef4f7f8554876495f8907d4f71e1152_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_{cilindro} =2\\pi r h + 2\\pi r^2 = 54\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"223\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u6211\u4eec\u6e05\u9664<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6868abdfd034048aa59644d2ac62353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd73c08d458b0ab2061031782d125ab9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\pi r h = 54 - 2\\pi r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"136\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-abf53b37d2a3ae4784079bfd67d3007f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h = \\cfrac{54 - 2\\pi r^2}{2\\pi r}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"112\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u66ff\u6362\u5728\u8981\u4f18\u5316\u7684\u51fd\u6570\u4e2d\u627e\u5230\u7684\u8868\u8fbe\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2c47f99ce14b444ed73661b2b568e8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V=  \\pi r^2 \\cdot h \\xrightarrow{h \\ = \\ \\frac{54 - 2\\pi r^2}{2\\pi r} } V = \\pi r^2 \\cdot \\cfrac{54 - 2\\pi r^2}{2\\pi r}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"346\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-81d564fcd7cdf880066ed3eb6eb9a18a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V = \\cancel{\\pi}  r^{\\cancel{2}} \\cdot \\cfrac{54 - 2\\pi r^2}{2 \\cancel{\\pi} \\cancel{r}} =r \\cdot \\cfrac{54 - 2\\pi r^2}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"278\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f95e7e1fc6088ba84a7b3885fe929d58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V(r) = r \\cdot (27 - \\pi r^2)= 27r - \\pi r^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"259\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5f85\u4f18\u5316\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-58e3403f2812564067058ece1bcd83ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V(r)=27r - \\pi r^3\\ \\longrightarrow \\ V'(r)= 27-3 \\pi r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"324\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u7b2c\u4e09\u6b65\uff1a\u627e\u5230\u5173\u952e\u70b9\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u627e\u5230\u51fd\u6570\u7684\u4e34\u754c\u70b9\uff0c\u6211\u4eec\u6c42\u89e3<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e868c9ed52907fbe13197b00c29b7d21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V'(r)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3de17aa96e46530402559cf14e8db4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V'(r)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10638a98b4a67b085c0854f95c86a65b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27-3 \\pi r^2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e31d335383816f692cd02cb2ca8f55b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3 \\pi r^2=-27\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"104\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ff57ef2a3aa07b3c9f9f76a9cb00f484_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r^2=\\cfrac{-27}{-3\\pi }\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"82\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d9e55eb22dc67a402b53bbb9ca17298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r^2=2,86\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8c7c4c4acf5b028e2dbba11dfc83d20b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{r^2}=\\sqrt{2,86}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"103\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01af3fa2bc910bd2da923aa2c83e1d7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r=1,69\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"67\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u6b65\u9aa44\uff1a\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u5e76\u786e\u5b9a\u51fd\u6570\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\uff0c\u6211\u4eec\u8868\u793a\u5728\u6570\u8f74\u4e0a\u627e\u5230\u7684\u4e34\u754c\u70b9\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-169.webp\" alt=\"\" class=\"wp-image-2508\" width=\"232\" height=\"90\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u786e\u5b9a\u51fd\u6570\u662f\u9012\u589e\u8fd8\u662f\u9012\u51cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u53d6\u4e00\u4e2a\u70b9\uff08\u4e0d\u662f\u4e34\u754c\u70b9\uff09\uff0c\u5e76\u67e5\u770b\u6b64\u65f6\u5bfc\u6570\u7684\u7b26\u53f7\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d2aa45b6cfc986ec1e33cdd5e9266e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V'(0)= 27-3 \\pi\\cdot 0^2 = 27-0 = +27 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"333\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c599118454ccdcc0e318f01ac61b84d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V'(2)= 27-3 \\pi \\cdot 2^2 = 27-37,70 = -10,70 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"393\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-169-positif-negatif.webp\" alt=\"\" class=\"wp-image-2509\" width=\"249\" height=\"176\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u589e\uff0c\u5982\u679c\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u51cf\u3002\u56e0\u6b64\uff0c\u589e\u957f\u533a\u95f4\u548c\u4e0b\u964d\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5e2776182fc7c0a5138adfee1aafaaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,1,69)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f4ac44f6269498e03069a77e1989c8be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,69,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u51fd\u6570\u5728 r=1.69 \u65f6\u4ece\u589e\u52a0\u53d8\u4e3a\u51cf\u5c11\uff0c\u56e0\u6b64<strong>r=1.69 cm \u662f\u8be5\u51fd\u6570\u7684\u6700\u5927\u503c<\/strong>\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0cr=1.69\u662f\u4f7f\u4f53\u79ef\u8fbe\u5230\u6700\u5927\u7684\u534a\u5f84\u503c\u3002\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u9ad8\u5ea6\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-381f3c5eb279572f486e28e68f0c5af2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h = \\cfrac{54 - 2\\pi \\cdot 1,69^2}{2\\pi \\cdot1,69} = \\cfrac{54 - 17,94}{10,62} = 3,39\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"316\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4f7f\u6700\u5927\u97f3\u91cf\u7684\u503c\u662f\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u6536\u97f3\u673a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c99f9d93c8a300be7afef76dfb71379_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{= r = 1,69} \\ \\mathbf{cm}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"117\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u9ad8\u5ea6<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ee2564c5e4b2a4e4409c392e5d01627_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{= h = 3,39} \\ \\mathbf{cm}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"119\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u4e00\u4e0b\u51fd\u6570\u4f18\u5316\u95ee\u9898\u662f\u5982\u4f55\u5206\u9636\u6bb5\u89e3\u51b3\u7684\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u89e3\u51b3\u4f18\u5316\u95ee\u9898\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 \u4ec0\u4e48\u662f\u4f18\u5316\u95ee\u9898 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/\"> <span class=\"screen-reader-text\">\u4f18\u5316\u95ee\u9898<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[17],"tags":[],"class_list":["post-42","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u4f18\u5316\u95ee\u9898\u2014\u2014<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/cn\/\u6700\u4f18\u5316\u95ee\u9898\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u4f18\u5316\u95ee\u9898\u2014\u2014\" \/>\n<meta property=\"og:description\" content=\"\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u4e00\u4e0b\u51fd\u6570\u4f18\u5316\u95ee\u9898\u662f\u5982\u4f55\u5206\u9636\u6bb5\u89e3\u51b3\u7684\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u89e3\u51b3\u4f18\u5316\u95ee\u9898\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 \u4ec0\u4e48\u662f\u4f18\u5316\u95ee\u9898 &hellip; \u4f18\u5316\u95ee\u9898 \u67e5\u770b\u5168\u6587 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/cn\/\u6700\u4f18\u5316\u95ee\u9898\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T10:57:01+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-optimisation-probleme.webp\" \/>\n<meta name=\"author\" content=\"Mathority\u56e2\u961f\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mathority\u56e2\u961f\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/\"},\"author\":{\"name\":\"Mathority\u56e2\u961f\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071\"},\"headline\":\"\u4f18\u5316\u95ee\u9898\",\"datePublished\":\"2023-09-17T10:57:01+00:00\",\"dateModified\":\"2023-09-17T10:57:01+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/\"},\"wordCount\":37,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/cn\/#organization\"},\"articleSection\":[\"\u51fd\u6570\u8868\u793a\"],\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/\",\"url\":\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/\",\"name\":\"\u4f18\u5316\u95ee\u9898\u2014\u2014\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/cn\/#website\"},\"datePublished\":\"2023-09-17T10:57:01+00:00\",\"dateModified\":\"2023-09-17T10:57:01+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/cn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u4f18\u5316\u95ee\u9898\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/cn\/#website\",\"url\":\"https:\/\/mathority.org\/cn\/\",\"name\":\"Mathority\",\"description\":\"\u597d\u5947\u5fc3\u4e0e\u8ba1\u7b97\u7684\u7ed3\u5408\uff01\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/cn\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/cn\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/cn\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/cn\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/cn\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/cn\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071\",\"name\":\"Mathority\u56e2\u961f\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g\",\"caption\":\"Mathority\u56e2\u961f\"},\"sameAs\":[\"http:\/\/mathority.org\/cn\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u4f18\u5316\u95ee\u9898\u2014\u2014","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/cn\/\u6700\u4f18\u5316\u95ee\u9898\/","og_locale":"zh_CN","og_type":"article","og_title":"\u4f18\u5316\u95ee\u9898\u2014\u2014","og_description":"\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u4e00\u4e0b\u51fd\u6570\u4f18\u5316\u95ee\u9898\u662f\u5982\u4f55\u5206\u9636\u6bb5\u89e3\u51b3\u7684\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u89e3\u51b3\u4f18\u5316\u95ee\u9898\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 \u4ec0\u4e48\u662f\u4f18\u5316\u95ee\u9898 &hellip; \u4f18\u5316\u95ee\u9898 \u67e5\u770b\u5168\u6587 &raquo;","og_url":"https:\/\/mathority.org\/cn\/\u6700\u4f18\u5316\u95ee\u9898\/","article_published_time":"2023-09-17T10:57:01+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-optimisation-probleme.webp"}],"author":"Mathority\u56e2\u961f","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"Mathority\u56e2\u961f"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/"},"author":{"name":"Mathority\u56e2\u961f","@id":"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071"},"headline":"\u4f18\u5316\u95ee\u9898","datePublished":"2023-09-17T10:57:01+00:00","dateModified":"2023-09-17T10:57:01+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/"},"wordCount":37,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/cn\/#organization"},"articleSection":["\u51fd\u6570\u8868\u793a"],"inLanguage":"zh-Hans","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/","url":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/","name":"\u4f18\u5316\u95ee\u9898\u2014\u2014","isPartOf":{"@id":"https:\/\/mathority.org\/cn\/#website"},"datePublished":"2023-09-17T10:57:01+00:00","dateModified":"2023-09-17T10:57:01+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/cn\/%e6%9c%80%e4%bc%98%e5%8c%96%e9%97%ae%e9%a2%98\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/cn\/"},{"@type":"ListItem","position":2,"name":"\u4f18\u5316\u95ee\u9898"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/cn\/#website","url":"https:\/\/mathority.org\/cn\/","name":"Mathority","description":"\u597d\u5947\u5fc3\u4e0e\u8ba1\u7b97\u7684\u7ed3\u5408\uff01","publisher":{"@id":"https:\/\/mathority.org\/cn\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/cn\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Organization","@id":"https:\/\/mathority.org\/cn\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/cn\/","logo":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/mathority.org\/cn\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/cn\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/cn\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/cn\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071","name":"Mathority\u56e2\u961f","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/mathority.org\/cn\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g","caption":"Mathority\u56e2\u961f"},"sameAs":["http:\/\/mathority.org\/cn"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/posts\/42","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/comments?post=42"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/posts\/42\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/media?parent=42"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/categories?post=42"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/tags?post=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}