{"id":356,"date":"2023-07-04T12:33:10","date_gmt":"2023-07-04T12:33:10","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%9c%89%e7%95%8c%e5%87%bd%e6%95%b0\/"},"modified":"2023-07-04T12:33:10","modified_gmt":"2023-07-04T12:33:10","slug":"%e6%9c%89%e7%95%8c%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%9c%89%e7%95%8c%e5%87%bd%e6%95%b0\/","title":{"rendered":"\u6709\u754c\u51fd\u6570"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u6709\u754c\uff08\u4e0a\u9650\u548c\u4e0b\u9650\uff09\u51fd\u6570\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c06\u5411\u60a8\u5c55\u793a\u51fd\u6570\u5728\u4e00\u70b9\u4e0a\u6709\u754c\u610f\u5473\u7740\u4ec0\u4e48\uff0c\u6700\u540e\u60a8\u5c06\u53d1\u73b0\u6b64\u7c7b\u51fd\u6570\u7684\u5c5e\u6027\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-acotada\"><\/span>\u4ec0\u4e48\u662f\u6709\u754c\u51fd\u6570\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6709\u754c\u51fd\u6570<\/strong>\u662f\u5176\u56fe\u5f62\u5728\u754c\u9650\u5185\u7684\u51fd\u6570\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u5b58\u5728\u6570\u5b57 K \u4e14\u4e0d\u5b58\u5728\u5927\u4e8e K (f(x)\u2264K) \u7684\u51fd\u6570\u503c\uff0c\u5219\u51fd\u6570\u5728\u4e0a\u65b9\u6709\u754c\uff1b\u5982\u679c\u5b58\u5728\u6570\u5b57 K \u4f7f\u5f97\u51fd\u6570\u5728\u4e0b\u65b9\u6709\u754c\uff0c\u5219\u51fd\u6570\u5728\u4e0b\u65b9\u6709\u754c\u5c0f\u4e8e\u51fd\u6570\u7684\u6240\u6709\u503c(f(x)\u2265K)\u3002\u56e0\u6b64\uff0c\u6709\u754c\u51fd\u6570\u662f\u4e0a\u4e0b\u6709\u754c\u7684\u51fd\u6570\u3002 <\/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\/fonction-bornee.webp\" alt=\"\u6709\u754c\u51fd\u6570\" class=\"wp-image-427\" width=\"481\" height=\"231\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4f8b\u5982\uff0c\u4e0a\u56fe\u6240\u793a\u7684\u4e09\u89d2\u6b63\u5f26\u51fd\u6570\u7684\u9876\u90e8\u8fb9\u754c\u4e3a f(x)=1\uff0c\u5e95\u90e8\u8fb9\u754c\u4e3a f(x)=-1\uff08\u7ea2\u8272\u865a\u7ebf\uff09\uff0c\u56e0\u4e3a\u51fd\u6570\u90fd\u5728\u8fd9\u4e24\u4e2a\u9650\u5236\u4e4b\u5185\u3002\u60a8\u53ef\u4ee5\u5728\u4ee5\u4e0b\u94fe\u63a5\u4e2d\u67e5\u770b\u8be5\u51fd\u6570\u7684\u66f4\u591a\u5c5e\u6027\uff1a<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6b63\u5f26\u51fd\u6570\/\">\u6b63\u5f26\u51fd\u6570\u7684\u7279\u6027<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-acotada-superiormente\"><\/span>\u4e0a\u9762\u6709\u754c\u7684\u51fd\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7136\u800c\uff0c\u5e76\u975e\u6240\u6709\u51fd\u6570\u90fd\u6709\u4e0a\u4e0b\u754c\uff0c\u51fd\u6570\u53ea\u80fd\u6709\u4e0a\u4e0b\u754c\u3002<\/p>\n<p><strong>\u4e0a\u8ff0\u6709\u754c\u51fd\u6570<\/strong>\u662f\u6307\u4e0d\u8d85\u8fc7\u67d0\u4e2a\u503c\u7684\u51fd\u6570\uff0c\u5373\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\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-d1b0912c8106b6c93144cda220414684_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\leq K\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5176\u4e2d K \u503c\u662f\u51fd\u6570\u7684\u4e0a\u9650\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u4e0b\u9762\u7684<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u4e8c\u6b21\u629b\u7269\u7ebf\u51fd\u6570\/\">\u629b\u7269\u7ebf<\/a><\/span>\u5728\u9876\u90e8\u4ee5 K=7 \u4e3a\u8fb9\u754c\uff0c\u4f46\u8be5\u51fd\u6570\u5728\u5e95\u90e8\u6ca1\u6709\u8fb9\u754c\uff0c\u56e0\u4e3a\u5b83\u7684\u5206\u652f\u5ef6\u4f38\u81f3\u65e0\u7a77\u5927\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-etape-par-etape-de-la-fonction-quadratique.webp\" alt=\"\" class=\"wp-image-139\" width=\"279\" height=\"334\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u5982\u679c\u51fd\u6570\u4ee5 K=7 \u4e3a\u754c\uff0c\u90a3\u4e48\u5b83\u4e5f\u4ee5 K=8 \u548c\u66f4\u9ad8\u503c\u4e3a\u754c\u3002<\/p>\n<p>\u6700\u5c0f\u7684\u4e0a\u754c\u79f0\u4e3a\u4e0a\u754c\uff0c\u7528<em>sup(f)<\/em>\u8868\u793a\u3002\u6b64\u5916\uff0c\u5982\u679c\u51fd\u6570\u5728\u5176\u5b9a\u4e49\u57df\u4e2d\u8fbe\u5230\u6240\u8ff0\u4e0a\u9650\uff0c\u6211\u4eec\u4f1a\u8bf4\u8be5\u70b9\u662f\u51fd\u6570\u7684<strong>\u7edd\u5bf9\u6700\u5927\u503c<\/strong>\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u770b\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u51fd\u6570\u76f8\u5bf9\u6781\u503c\u7684\u6781\u5927\u6781\u5c0f\u503c\/\">\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u662f\u591a\u5c11\uff1f<\/a><\/span><\/p>\n<p>\u5728\u6211\u4eec\u7684\u4f8b\u5b50\u4e2d\uff0c\u51fd\u6570\u7684\u51e0\u4f55\u8fb9\u754c\u4e3a K=7\uff0c\u56e0\u6b64\u5b83\u662f\u51fd\u6570\u7684\u4e0a\u6781\u503c\u548c\u7edd\u5bf9\u6700\u5927\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-acotada-inferiormente\"><\/span>\u4e0b\u9762\u5206\u9694\u7684\u51fd\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4e0b\u9762\u754c\u5b9a\u7684\u51fd\u6570<\/strong>\u662f\u90a3\u4e9b\u503c\u4e0d\u5c0f\u4e8e\u67d0\u4e2a\u6570\u5b57\u7684\u51fd\u6570\uff0c\u5373\u5b83\u4eec\u6ee1\u8db3\u4ee5\u4e0b\u6570\u5b66\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-6428bb46a6513be54693aaeb3c70fdc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\geq K\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5176\u4e2dK\u503c\u662f\u51fd\u6570\u7684\u4e0b\u754c\u3002<\/p>\n<p>\u4e0b\u9762\u662f\u6307\u6570\u51fd\u6570\u7684\u56fe\u5f62\u8868\u793a\uff0c\u4e0b\u9762\u7528 K=3 \u5206\u9694\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\/probleme-de-fonction-exponentielle.webp\" alt=\"\" class=\"wp-image-253\" width=\"264\" height=\"321\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u663e\u7136\uff0c\u8be5\u51fd\u6570\u4e5f\u53d7\u5230\u5c0f\u4e8e K=3 \u7684\u503c\u7684\u9650\u5236\u3002<\/p>\n<p>\u5982\u524d\u6240\u8ff0\uff0c\u6700\u5927\u4e0b\u754c\u79f0\u4e3a\u4e0b\u754c\uff0c\u7528<em>inf(f)<\/em>\u8868\u793a\u3002\u6b64\u5916\uff0c\u5982\u679c\u51fd\u6570\u5728\u5176\u5b9a\u4e49\u57df\u4e2d\u8fbe\u5230\u6240\u8ff0\u4e0b\u6781\u503c\uff0c\u6211\u4eec\u4f1a\u8bf4\u8be5\u70b9\u662f\u51fd\u6570\u7684<strong>\u7edd\u5bf9\u6700\u5c0f\u503c<\/strong>\u3002<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0cK=3 \u4e0d\u662f\u51fd\u6570\u7684\u7edd\u5bf9\u6700\u5c0f\u503c\uff0c\u56e0\u4e3a\u51fd\u6570\u5728\u65e0\u7a77\u8fdc\u5904\u8fbe\u5230\u8be5\u503c\uff0c\u56e0\u6b64\u5b83\u5728\u5176\u57df\u4e4b\u5916\u3002\u6362\u53e5\u8bdd\u8bf4\uff0cf(x)=3 \u662f<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6c34\u5e73\u6e10\u8fd1\u7ebf\/\">\u51fd\u6570 \u7684\u6c34\u5e73\u6e10\u8fd1\u7ebf<\/a><\/span>\u3002<\/p>\n<p>\u6709\u4e00\u4e2a\u5b9a\u7406\u53ef\u4ee5\u8ba9\u60a8\u77e5\u9053\u51fd\u6570\u662f\u5426\u5728\u9876\u90e8\u548c\u5e95\u90e8\u6709\u754c\uff0c\u800c\u65e0\u9700\u5176\u56fe\u5f62\u8868\u793a\u3002\u5355\u51fb\u6b64\u5904\u67e5\u770b\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u662f\u4ec0\u4e48\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u89c1\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u5fb7\u5a01\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\/\">\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-acotada-en-un-punto\"><\/span>\u51fd\u6570\u6709\u754c\u4e8e\u4e00\u70b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6211\u4eec\u521a\u521a\u7814\u7a76\u4e86\u4e00\u822c\u51fd\u6570\u6709\u754c\u7684\u6982\u5ff5\uff0c\u4f46\u4e5f\u53ef\u4ee5\u5206\u6790\u51fd\u6570\u662f\u5426\u5728\u8f83\u5c0f\u7684\u90bb\u57df\u5185\uff08\u5373\u51fd\u6570\u7684\u4e00\u90e8\u5206\uff09\u6709\u754c\u3002<\/p>\n<p>\u662f\u7684<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u51fd\u6570\u57df\u4e2d\u7684\u4e00\u4e2a\u70b9\u5e76\u4e14<\/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>\u4efb\u4f55\u503c\uff0c\u6211\u4eec\u90fd\u4f1a\u8bf4\u8be5\u51fd\u6570\u5728\u8be5\u70b9\u7684\u4e0a\u65b9\/\u4e0b\u65b9\u6709\u754c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5982\u679c\u6709\u4e00\u4e2a\u73af\u5883<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35809b342e97743c17fcf00c8f1fcaa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V(a,r)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5176\u4e2d\u51fd\u6570\u5728\u4e0a\u65b9\/\u4e0b\u65b9\u6709\u754c\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u51fd\u6570\u6709\u754c\u4e8e\u70b9<\/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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5982\u679c\u5b83\u662f\u5728\u90bb\u57df\u7684\u9876\u90e8\u548c\u5e95\u90e8\u754c\u5b9a\u7684<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bad21933de1c285515285d51686beea1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V(a,r).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u663e\u7136\uff0c\u5982\u679c\u4e00\u4e2a\u51fd\u6570\u603b\u4f53\u4e0a\u662f\u6709\u754c\u7684\uff0c\u90a3\u4e48\u5b83\u5728\u5b83\u7684\u6bcf\u4e2a\u70b9\u4e0a\u4e5f\u5c06\u662f\u6709\u754c\u7684\u3002\u7136\u800c\uff0c\u76f8\u53cd\u7684\u60c5\u51b5\u662f\u9519\u8bef\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u51fd\u6570\u53ef\u4ee5\u5728\u5176\u6bcf\u4e2a\u70b9\u4e0a\u6709\u754c\uff0c\u4f46\u4e0d\u80fd\u5728\u5176\u6574\u4e2a\u57df\u4e0a\u6709\u754c\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u4ee5\u4e0b\u4eff\u5c04\u51fd\u6570\u5728\u5176\u6bcf\u4e2a\u70b9\u5904\u90fd\u6709\u90e8\u5206\u6709\u754c\uff0c\u4f46\u5b83\u4e0d\u662f\u6709\u754c\u51fd\u6570\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-representation-d-une-fonction-lineaire-ou-affine.webp\" alt=\"\" class=\"wp-image-104\" width=\"263\" height=\"265\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-las-funciones-acotadas\"><\/span>\u6709\u754c\u51fd\u6570\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6709\u754c\u51fd\u6570\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a<\/p>\n<ul>\n<li>\u662f\u7684\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a5054ad96fb0978182340eb214bb125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u4e24\u4e2a\u6709\u754c\u51fd\u6570\uff0c\u4e24\u4e2a\u51fd\u6570\u7684\u52a0\uff08\u6216\u51cf\uff09<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e24299805ed877ea052cd135c96e7c28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\pm g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u4e5f\u662f\u6709\u754c\u51fd\u6570\u3002<\/li>\n<li>\u662f\u7684\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: 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