{"id":1465,"date":"2024-04-09T20:05:15","date_gmt":"2024-04-09T12:05:15","guid":{"rendered":"http:\/\/jiaohuweike.online\/?p=1465"},"modified":"2024-04-09T20:05:15","modified_gmt":"2024-04-09T12:05:15","slug":"hsyldwt-5","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=1465","title":{"rendered":"\u5bfc\u6570\u7efc\u5408\u9898-\u57fa\u7840\u7bc7"},"content":{"rendered":"\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-711932c\" data-block-id=\"711932c\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">\u5df2\u77e5\u51fd\u6570\u5355\u8c03\u6027\u6c42\u53c2\u6570\u8303\u56f4<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\u82e5\u51fd\u6570  f(x)  \u662f\u5b9a\u4e49\u57df  D  \u5185\u67d0\u4e2a\u533a\u95f4  I  \u4e0a\u7684\u589e\u51fd\u6570, \u4e14  F(x)=\\frac{f(x)}{x}  \u5728  I  \u4e0a\u662f\u51cf\u51fd\u6570, \u5219~~~~\\\\\u79f0\u51fd\u6570  f(x)  \u662f  I  \u4e0a\u7684 \u201c\u5355\u53cd\u51cf\u51fd\u6570\u201d. \u5df2\u77e5  f(x)=\\ln x ,  g(x)=2 x+\\frac{2}{x}+a \\ln x(a \\in \\mathbf{R}) .~~~~~~\\\\\n(1) \u5224\u65ad\u51fd\u6570  f(x)  \u5728  (0,1)  \u5185\u662f\u4e0d\u662f \u201c\u5355\u53cd\u51cf\u51fd\u6570\u201d;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(2) \u82e5\u51fd\u6570  g(x)  \u662f  [1,+\\infty)  \u4e0a\u7684 \u201c\u5355\u53cd\u51cf\u51fd\u6570\u201d,\u6c42\u5b9e\u6570  a  \u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(1)\u4e0d\u662f\u5355\u53cd\u51cf\u51fd\u6570\uff082\uff090\\le a\\le4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-6de6d64\" data-block-id=\"6de6d64\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-efb1d37\" data-block-id=\"efb1d37\"><style>.stk-efb1d37 .stk-button{border-top-left-radius:11px !important;border-top-right-radius:11px !important;border-bottom-right-radius:11px !important;border-bottom-left-radius:11px !important}.stk-efb1d37 .stk-button:before{box-shadow:0 0 0 2px #7878781a !important}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E5%AF%BC%E6%95%B0%E7%BB%BC%E5%90%88%E7%BB%83%E4%B9%A0%E5%9F%BA%E7%A1%801\/HTML5\/practice.html\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u89c2\u770b\u5fae\u8bfe<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u653e\u7f29\u4e00\u4e2a\u91cf\u8bc1\u660e\u4e0d\u7b49\u5f0f<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u51fd\u6570f(x)=e^x-2x+2a.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u6c42\u8bc1\uff1a\u5f53a&gt;ln2-1\u4e14x&gt;0\u65f6\uff0ce^x&gt;x^2-2ax+1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-e13c9bd\" data-block-id=\"e13c9bd\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-2329337\" data-block-id=\"2329337\"><style>.stk-2329337 .stk-button{border-top-left-radius:11px !important;border-top-right-radius:11px !important;border-bottom-right-radius:11px !important;border-bottom-left-radius:11px !important}.stk-2329337 .stk-button:before{box-shadow:0 0 0 2px #7878781a !important}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E5%AF%BC%E6%95%B0%E7%BB%BC%E5%90%88%E9%A2%98%E5%9F%BA%E7%A1%802\/HTML5\/practice.html\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u89c2\u770b\u5fae\u8bfe<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e601\uff1a\u5df2\u77e5f(x)=\\frac{ax^2+x-1}{e^x} ,\u6c42\u8bc1\uff1a\u5f53a\\ge 1\u65f6\uff0cf(x)+e\\ge 0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u53ea\u9700\u8bc1\u660ea=1\u65f6\uff0cf(x)+e\\ge 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e602\uff1a\u5f53x&gt;0\u65f6\uff0c\u8bc1\u660e\uff1ae^x-\\sin x-1&gt;x\\ln x.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u63d0\u793a\uff1a\u5148\u653e\u7f29,\u5f53x&gt;0\u65f6,x&gt;\\sin x.\u53ea\u9700\u8bc1e^x-x-1&gt;x\\ln x,\u4ee4f(x)=e^x-x-1-~~\\\\x\\ln x,f'(x)=e^x-\\ln x-2,f''(x)=e^x-\\frac{1}{x},f''(\\frac{1}{2})=\\sqrt{e}-2&lt;0,f''(1)&gt;0,\\therefore \\exists x_0\\in\\\\ (\\frac{1}{2},1) ,\u5373e^{x_0}=\\frac{1}{x_0} ,f''(x_0)=0,\\therefore f'(x)\u7684\u6781\u5c0f\u503c\u4e3af'(x_0)=e^{x_0}-\\ln{x_0}-2=~~~~~~~~~~~~~~~~~~\\\\x_0+\\frac{1}{x_0}-2&gt;0,\\therefore f'(x)\\ge f'(x_0)&gt;0,\\therefore f(x)\u5728(0,+\\infty )\u5355\u589e\uff0cf(x)&gt;f(0)=~~~~~~~~~~~~~~\\\\\\lim_{x \\to 0} x\\ln x=\\lim_{x \\to 0} \\frac{(\\ln x)'}{(\\frac{1}{x})' } =\\lim_{x \\to 0} x=0,\\therefore f(x)&gt;0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-6e3b8c6\" data-block-id=\"6e3b8c6\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-fc9027d\" data-block-id=\"fc9027d\"><style>.stk-fc9027d{border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E5%AF%BC%E6%95%B0%E6%8F%90%E9%AB%982-2\/HTML5\/practice.html\"><span class=\"stk-button__inner-text\">\u89c2\u770b\u5fae\u8bfe<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e603\uff1a\u5df2\u77e5\u51fd\u6570f(x)=ae^x-\\ln x-1,\u8bc1\u660e\uff1a\u5f53a\\ge\\frac{1}{e}\u65f6\uff0cf(x)\\ge0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u63d0\u793a\uff1a\u53ea\u9700\u8bc1\u660ea=\\frac{1}{e}\u65f6\uff0cf(x)\\ge 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u5206\u79bb\u53c2\u91cf\u5e76\u731c\u6839<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u8bbef(x)=ax+ax\\ln x,a&gt;0.\u82e5\u5bf9\u4e8e\\forall x\\in [\\frac{1}{2},+\\infty ),\u6709f(x)\\le e^{2x}\u6052\u6210\u7acb\uff0c\u6c42a\u7684~~~~~~~~~\\\\\u6700\u5927\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a\\le e^2,\u6240\u4ee5a\u7684\u6700\u5927\u503c\u4e3ae^2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-1dda9ec\" data-block-id=\"1dda9ec\"><style>.stk-1dda9ec{height:30px !important}<\/style><\/div>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-38fe971\" data-block-id=\"38fe971\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-cd579de\" data-block-id=\"cd579de\"><style>.stk-cd579de .stk-button{border-top-left-radius:11px !important;border-top-right-radius:11px !important;border-bottom-right-radius:11px !important;border-bottom-left-radius:11px !important}.stk-cd579de .stk-button:before{box-shadow:0 0 0 2px #7878781a !important}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E5%87%BD%E6%95%B0%E7%BB%BC%E5%90%88%E9%A2%98%E2%80%94%E2%80%94%E5%9F%BA%E7%A1%804\/HTML5\/practice.html\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u89c2\u770b\u5fae\u8bfe<\/span><\/a><\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5206\u79bb\u53c2\u91cf\u5e76\u731c\u6839<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[50],"class_list":["post-1465","post","type-post","status-publish","format-standard","hentry","category-4","tag-50"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1465","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1465"}],"version-history":[{"count":0,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1465\/revisions"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1465"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1465"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}