{"id":1429,"date":"2024-04-07T18:21:26","date_gmt":"2024-04-07T10:21:26","guid":{"rendered":"http:\/\/jiaohuweike.online\/?p=1429"},"modified":"2024-04-07T18:21:26","modified_gmt":"2024-04-07T10:21:26","slug":"hsyldwt-4","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=1429","title":{"rendered":"\u5bfc\u6570\u4e0e\u5355\u8c03\u6027"},"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\">\u6839\u636e\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.(1)\u82e5\u51fd\u6570f(x)\uff1dx^3\uff0bax^2+x\u5728R\u4e0a\u5355\u8c03\u9012\u589e\uff0c\u6c42\u5b9e\u6570a\u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\~~~(2)\u82e5\u51fd\u6570f(x)\uff1dx^3\uff0bax^2+x\u5728(0,+\\infty)\u4e0a\u5355\u8c03\u9012\u589e\uff0c\u6c42\u5b9e\u6570a\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>\u7b54\u6848:(1)[-\\sqrt3,\\sqrt3],(2)a\\ge -\\sqrt3;\u63d0\u793a\uff1a(1)\\triangle \\le0;(2)\u5206\u79bba.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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>2. \u82e5\u51fd\u6570  f(x)=\\left(x^{2}-m x+2\\right) \\mathrm{e}^{x}  \u5728  \\left[-\\frac{1}{2}, 1\\right]  \u4e0a\u5b58\u5728\u5355\u8c03\u9012\u51cf\u533a\u95f4, \u6c42  m  \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>\u7b54\u6848\uff1am&gt;2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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>3.\u8bbe  a \\in(0,1) , \u82e5\u51fd\u6570  f(x)=a^{x}+(1+a)^{x}  \u5728  (0,+\\infty)  \u4e0a\u5355\u8c03\u9012\u589e, \u6c42  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>\u7b54\u6848\uff1a[\\frac{\\sqrt5-1}{2},1)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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-b35f8fa\" data-block-id=\"b35f8fa\"><style>.stk-b35f8fa{margin-bottom:82px !important}<\/style><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-c8846ea\" data-block-id=\"c8846ea\"><style>.stk-c8846ea{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%87%BD%E6%95%B0%E5%8D%95%E8%B0%83%E6%80%A7%E3%80%81%E6%9E%81%EF%BC%88%E6%9C%80%EF%BC%89%E5%80%BC-3\/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<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u82e5\u51fd\u6570  f(x)=2 x^{2}-\\ln x  \u5728\u5176\u5b9a\u4e49\u57df\u7684\u4e00\u4e2a\u5b50\u533a\u95f4  (2 k-1,2 k+1)  \u5185\u4e0d\u5355\u8c03, \u6c42~~~~~~~~~~\\\\\u5b9e\u6570  k  \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<br><\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7b54\u6848:  \\left[\\frac{1}{2}, \\frac{3}{4}\\right)  ;\u63d0\u793a:f(x)  \u7684\u5b9a\u4e49\u57df\u4e3a  (0,+\\infty) , \u5219  2 k-1 \\geqslant 0 , \u5373  k \\geqslant \\frac{1}{2} ,f^{\\prime}(x)=4 x-\\frac{1}{x}\\\\=\\frac{4 x^{2}-1}{x}=\\frac{(2 x+1)(2 x-1)}{x},\n\n\n\u56e0\u4e3a  f(x)  \u5728  (2 k-1,2 k+1)  \u5185\u4e0d\u5355\u8c03, \u6240\u4ee5 ~~~~~~~~~~~~~~~~~~~~~\\\\ 2 k-1&lt; \\frac{1}{2}&lt;2 k+1 , \u5f97  -\\frac{1}{4 }&lt; k &lt; \\frac{3}{4} ,\u7efc\u4e0a,  \\frac{1}{2} \\leqslant k&lt;\\frac{3}{4} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-stackable-heading stk-block-heading stk-block-heading--v2 stk-block stk-fa21366\" id=\"\u8ba8\u8bba\u5355\u8c03\u6027\" data-block-id=\"fa21366\"><h4 class=\"stk-block-heading__text\">\u8ba8\u8bba\u5355\u8c03\u6027<\/h4><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\u5df2\u77e5\u51fd\u6570f(x)=ax-\\ln x-1,a\\in R.\u8ba8\u8bbaf(x)\u7684\u5355\u8c03\u6027.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u5df2\u77e5\u51fd\u6570f(x)=e^x(x^2+2ax+2a),a\\in R.\u8ba8\u8bbaf(x)\u7684\u5355\u8c03\u6027.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u5df2\u77e5\u51fd\u6570f(x)=\\frac{1}{2}x^2-\\frac{a^2+1}{a}x+\\ln x,a\\in R.\u8ba8\u8bbaf(x)\u7684\u5355\u8c03\u6027.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\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\/%E8%AE%A8%E8%AE%BA%E5%87%BD%E6%95%B0%E5%8D%95%E8%B0%83%E6%80%A71-3\/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<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u5df2\u77e5\u51fd\u6570  f(x)=\\frac{1}{2} a x^{2}-(a+1) x+\\ln x,  \u8bd5\u8ba8\u8bba\u51fd\u6570  y=f(x)  \u7684\u5355\u8c03\u6027.~~~~~~~~~~~~~~~~~~~~~~<\/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>\u7b54\u6848\uff1a(1)\u5f53a\\le 0\u65f6\uff0c f(x)  \u5728  (0,1)\u5355\u8c03\u9012\u589e\uff0c\u5728 (1,+\\infty)\u5355\u8c03\u9012\u51cf\uff1b(2)\u5f53  0&lt; a &lt;1  \u65f6, \\\\\u51fd\u6570  f(x)  \u5728  (0,1)  \u548c  \\left(\\frac{1}{a},+\\infty\\right)  \u4e0a\u5355\u8c03\u9012\u589e, \u5728  \\left(1, \\frac{1}{a}\\right)  \u4e0a\u5355\u8c03\u9012\u51cf;(3)\u5f53  a=1  \u65f6, \u51fd\u6570 ~~\\\\ f(x)  \u5728  (0,+\\infty)  \u4e0a\u5355\u8c03\u9012\u589e;(4)\n\n\u5f53  a&gt;1  \u65f6, \u51fd\u6570  f(x)  \u5728  \\left(0, \\frac{1}{a}\\right) \u548c  (1,+\\infty)  \u4e0a\u5355\u8c03\u9012\u589e, ~~~\\\\\u5728  \\left(\\frac{1}{a}, 1\\right)  \u4e0a\u5355\u8c03\u9012\u51cf.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u63d0\u793a\uff1a\u51fd\u6570  f(x)  \u7684\u5b9a\u4e49\u57df\u4e3a  (0,+\\infty) ,f^{\\prime}(x)=a x-(a+1)+\\frac{1}{x} \n=\\frac{a x^{2}-(a+1) x+1}{x}~~~\\\\=\\frac{(a x-1)(x-1)}{x} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n<\/details>\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>5.\u5df2\u77e5\u51fd\u6570f(x)=x^3-ax^2+3x+1,a\\in R.\u8ba8\u8bbaf(x) \u7684\u5355\u8c03\u6027.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>6.\u5df2\u77e5\u51fd\u6570f(x)=a\\ln x-x^2+3x+3a,a\\in R.\u8ba8\u8bbaf(x)\u7684\u5355\u8c03\u6027.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-af3694e\" data-block-id=\"af3694e\"><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-07efcb7\" data-block-id=\"07efcb7\"><style>.stk-07efcb7 .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-07efcb7 .stk-button:before{box-shadow:0 0 0 2px #7878781a !important}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E8%AE%A8%E8%AE%BA%E5%87%BD%E6%95%B0%E5%8D%95%E8%B0%83%E6%80%A74-5\/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>7.\u5df2\u77e5\u51fd\u6570f(x)=ax-\\frac{\\sin x}{\\cos^3x},x\\in(0,\\frac{\\pi}{2}),a=8\u65f6\uff0c\u6c42f(x)\u7684\u5355\u8c03\u533a\u95f4.~~~~~~~~~~~~~~~~~~~~~~~~<\/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>\u7b54\u6848\uff1af(x)\u5728(0,\\frac{\\pi}{4})\u5355\u589e\uff0c\u5728(\\frac{\\pi}{4},\\frac{\\pi}{2})\u5355\u51cf\uff1b\u63d0\u793a\uff1af'(x)=\\frac{(2\\cos^2x-1)(4\\cos^2x+3)}{\\cos^4x},~\\\\x\\in(0,\\frac{\\pi}{4}),f'(x)&lt;0,x\\in(\\frac{\\pi}{4},\\frac{\\pi}{2}),f'(x)&gt;0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n","protected":false},"excerpt":{"rendered":"<p>\u5bfc\u6570\u4e3a\u4e00\u6b21\u6216\u4e8c\u6b21\u53ef\u5206\u89e3\u578b<\/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":[21,24],"class_list":["post-1429","post","type-post","status-publish","format-standard","hentry","category-4","tag-21","tag-24"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1429","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=1429"}],"version-history":[{"count":0,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1429\/revisions"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1429"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}