{"id":1502,"date":"2024-04-11T20:50:28","date_gmt":"2024-04-11T12:50:28","guid":{"rendered":"http:\/\/jiaohuweike.online\/?p=1502"},"modified":"2024-04-11T20:50:28","modified_gmt":"2024-04-11T12:50:28","slug":"hsyldwt-5-2","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=1502","title":{"rendered":"\u6839\u636e\u5bfc\u6570\u5173\u7cfb\u5f0f\u6784\u9020\u51fd\u6570"},"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<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u5e38\u89c1\u7684\u6784\u9020\u6a21\u578b<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1. \u82e5\u5df2\u77e5f^{\\prime}(x)+f(x) , \u6784\u9020\u51fd\u6570  F(x)=e^{x} f(x);~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u82e5 \u5df2\u77e5 f^{\\prime}(x)-f(x)\uff0c\u6784\u9020\u51fd\u6570  F(x)=\\frac{f(x)}{e^{x}}\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u82e5\u5df2\u77e5x f^{\\prime}(x)+f(x),\u6784\u9020\u51fd\u6570  F(x)=x f(x) \uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u82e5 \u5df2\u77e5 x f^{\\prime}(x)-f(x) , \u6784\u9020\u51fd\u6570  F(x)=\\frac{f(x)}{x}(x \\neq 0)\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.\u82e5\u5df2\u77e5f^{\\prime}(x) \\sin x+f(x) \\cos x    , \u6784\u9020\u51fd\u6570 F(x)=f(x) \\sin x;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>6.\u82e5\u5df2\u77e5f^{\\prime}(x) \\sin x-f(x) \\cos x  ,\u6784\u9020\u51fd\u6570 F(x)=\\frac{f(x)}{\\sin x};~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>7.\u82e5\u5df2\u77e5 f^{\\prime}(x) \\cos x-f(x) \\sin x   , \u6784\u9020\u51fd\u6570 F(x)=f(x) \\cos x  ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>8.\u82e5\u5df2\u77e5f^{\\prime}(x) \\cos x+f(x) \\sin x  , \u6784\u9020\u51fd\u6570 F(x)=\\frac{f(x)}{\\cos x}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-stackable-heading stk-block-heading stk-block-heading--v2 stk-block stk-fa21366\" id=\"\u9898\u76ee\" data-block-id=\"fa21366\"><h4 class=\"stk-block-heading__text\">\u9898\u76ee<\/h4><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e601\uff1a\u51fd\u6570f(x)\u7684\u5bfc\u51fd\u6570\u4e3a{f}'(x),\u5bf9\u4efb\u610f\u7684x&gt;0,\u90fd\u6709{f}'(x)&gt;\\frac{2}{x},  \u4e14f(e)=3,\u6c42\u4e0d\u7b49\\\\\u5f0ff(x)&gt;2\\ln x+1\u7684\u89e3\u96c6.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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:(e,+\\infty);\u63d0\u793a:\u6784\u9020F(x)=f(x)-2\\ln x \n -1,F'(x)&gt;0,F(e)=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\u5df2\u77e5\u51fd\u6570f(x)\u53ca\u5176\u5bfc\u6570{f}'(x)\u5b9a\u4e49\u57df\u90fd\u662fR\uff0c\u4e14f(x)-{f}'(x)&gt;0,f(0)=1,\u6c42~~~\\\\\u4e0d\u7b49\u5f0ff(x)&gt;e^x\u7684\u89e3\u96c6.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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:(-\\infty,0);\u63d0\u793a:\u6784\u9020F(x)=\\frac{f(x)}{e^x}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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\u4e603\uff1a\u8bbef(x),g(x)\u5206\u522b\u662f\u5b9a\u4e49\u5728R\u4e0a\u7684\u5947\u51fd\u6570\u548c\u5076\u51fd\u6570\uff0c\u5f53x&lt;0\u65f6\uff0c{f}'(x)g(x)-~~~~\\\\f(x){g}'(x)&gt;0,\u4e14f(3)=0,g(x)\\ne 0,\u6c42\u4e0d\u7b49\u5f0ff(x)g(x)&gt;0\u7684\u89e3\u96c6\u3002~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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:(-3,0)\\cup (3,+\\infty );\u63d0\u793a:\u6784\u9020F(x)=\\frac{f(x)}{g(x)},f(x)g(x)&gt;0\u4e0e\\frac{f(x)}{g(x)}&gt;0\u540c\u89e3.~~~~~~~~~<\/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-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\"><style>.stk-38fe971 .stk-button-group{flex-direction:row !important;}@media screen and (max-width:999px){.stk-38fe971 .stk-button-group{flex-direction:row !important;}}@media screen and (max-width:689px){.stk-38fe971 .stk-button-group{flex-direction:row !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-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\/%E7%94%B1%E5%AF%BC%E6%95%B0%E5%85%B3%E7%B3%BB%E6%9E%84%E9%80%A0%E5%87%BD%E6%95%B0\/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<h4 class=\"wp-block-heading\">\u5de9\u56fa<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u5b9a\u4e49\u5728  \\left(0, \\frac{\\pi}{2}\\right)  \u4e0a\u7684\u51fd\u6570  f(x) \u7684\u5bfc\u51fd\u6570\u4e3a  f^{\\prime}(x) , \u4e14\u6052\u6709  \\cos x \\cdot f^{\\prime}(x)+\\sin x \\cdot f(x)&lt;0 ~~\\\\ \u6210\u7acb, \u5219\u4e0b\u5217\u9009\u9879\u6b63\u786e\u7684\u662f (\\quad)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\\\\nA.  f\\left(\\frac{\\pi}{6}\\right)&gt;\\sqrt{2} f\\left(\\frac{\\pi}{4}\\right) ~~~~~~~~~~~~~~~~~~~~~~~~~~\nB.  \\sqrt{3} f\\left(\\frac{\\pi}{6}\\right)&gt;f\\left(\\frac{\\pi}{3}\\right) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nC.  f\\left(\\frac{\\pi}{6}\\right)&gt;\\sqrt{3} f\\left(\\frac{\\pi}{3}\\right) ~~~~~~~~~~~~~~~~~~~~~~~~~~\nD.  \\sqrt{2} f\\left(\\frac{\\pi}{6}\\right)&gt;\\sqrt{3} f\\left(\\frac{\\pi}{4}\\right) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n<\/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\uff1aCD;\u63d0\u793a\uff1a\u6784\u9020\u51fd\u6570F(x)=\\frac{f(x)}{\\cos x}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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>5.\u5df2\u77e5  f(x)  \u5728  \\mathrm{R}  \u4e0a\u662f\u5947\u51fd\u6570, \u4e14  f^{\\prime}(x)  \u4e3a  f(x)  \u7684\u5bfc\u51fd\u6570, \u5bf9\u4efb\u610f  x \\in \\mathrm{R} , \u5747\u6709  f(x)&gt;\\frac{f^{\\prime}(x)}{\\ln 2}  ~~~~\\\\\u6210\u7acb,\u82e5  f(-2)=2 , \u5219\u4e0d\u7b49\u5f0f  f(x)&gt;-2^{x-1}  \u7684\u89e3\u96c6\u4e3a  (\\quad) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.  (-2,+\\infty) ~~~~~~\nB.  (2,+\\infty) ~~~~~~\nC.  (-\\infty,-2) ~~~~~~\nD.  (-\\infty, 2) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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\uff1aD\uff1b\u63d0\u793a\uff1a\u6784\u9020\u51fd\u6570F(x)=\\frac{f(x)}{2^x}+\\frac{1}{2},f(2)=-2,F(2)=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>6.\u5b9a\u4e49\u5728  (0,+\\infty)  \u4e0a\u7684\u51fd\u6570  f(x)  \u6ee1\u8db3  2 f(x)+x f^{\\prime}(x)=\\frac{1}{x^{2}}, f(1)=0 \uff08  \u82e5  f^{\\prime}(x)=\\frac{1}{x} , ~~~~~~~~\\\\\u5219  f(x)=   \\ln x+c, c  \u4e3a\u5e38\u6570), \u6bd4\u8f83  f(1), f(\\sqrt{2}), f(\\sqrt{3})  \u7684\u5927\u5c0f~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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(1)&lt; f(\\sqrt{2})&lt; f(\\sqrt{3});\u63d0\u793a\uff1a\u75312 f(x)+x f^{\\prime}(x)=\\frac{1}{x^{2}}\u5f972 xf(x)+x ^2f^{\\prime}(x)=\\frac{1}{x},\\\\\u6784\u9020F(x)=x^2f(x)=\\ln x,\u6240\u4ee5f(x)=\\frac{\\ln x}{x^2},\u4e14f(\\sqrt{2})=f(2).\u7531\u5355\u8c03\u6027\u53ef\u63a8\u5f97.~~~~~~~~~~~~~<\/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>7. \u5df2\u77e5  f(x)  \u662f\u5b9a\u4e49\u5728  (-\\infty, 0) \\cup(0,+\\infty)  \u4e0a\u7684\u5947\u51fd\u6570, \u5f53  x&gt;0  \u65f6,  f(x)+x f^{\\prime}(x)&gt;0  \u4e14 ~~~~~\\\\ f(2)=\\frac{1}{2} , \u5219\u4e0d\u7b49\u5f0f  f(x)&gt;\\frac{1}{x}  \u7684\u89e3\u96c6\u662f (~~~~~~ )~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.  (-2,0) \\cup(0,2) ~~~\nB.  (-\\infty,-2) \\cup(2,+\\infty) ~~~\nC.  (-\\infty,-2)\\cup (0,2) ~~~\nD.  (-2,0) \\cup (2,+\\infty) <\/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\uff1aD\uff1b\u63d0\u793a\uff1a\u8981\u89e3f(x)&gt;\\frac{1}{x} \uff0c\u53ea\u9700\u89e3\\frac{xf(x)-1}{x}&gt;0,\u6784\u9020F(x)=xf(x)-1,~~~~~~~~~\\\\\u5219F(x)\u4e3a\u5076\u51fd\u6570\uff0c\u5728(0,\\infty)\u5355\u589e\u3002~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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>8.\u5df2\u77e5\u5b9a\u4e49\u5728  \\mathbf{R}  \u4e0a\u7684\u51fd\u6570  f(x)  \u7684\u5bfc\u51fd\u6570\u4e3a  f^{\\prime}(x) , \u5f53  x&gt;0  \u65f6,  x f^{\\prime}(x)-f(x)&gt;0 , \u82e5~~~~~~~~~~~ \\\\ a=f(1), b=\\frac{f(2)}{2}, c=2 f\\left(\\frac{1}{2}\\right) , \u6c42  a, b, c  \u7684\u5927\u5c0f\u5173\u7cfb.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/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:  c&lt; a&lt; b ;\u63d0\u793a\uff1a\u6784\u9020\u51fd\u6570  g(x)=\\frac{f(x)}{x}(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-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>9. \u5df2\u77e5\u51fd\u6570  f(x)  \u7684\u5bfc\u51fd\u6570\u4e3af^{\\prime}(x) , \u4e14  f(x)+f^{\\prime}(x)&gt;0  \u5728  \\mathbf{R}  \u4e0a\u6052\u6210\u7acb, \u6c42\u4e0d\u7b49\u5f0f  ~~~~~~~~~~~~~~~~~\\\\\\mathrm{e}^{2 x+1} f(2 x+1)&gt;\\mathrm{e}^{3-x} f(3-x)  \u7684\u89e3\u96c6.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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:\\left(\\frac{2}{3},+\\infty\\right) ;\n\u89e3\u6790: \u4ee4  g(x)=\\mathrm{e}^{x} f(x) ,g^{\\prime}(x)&gt;0,\u53ea\u9700\u89e3  g(2 x+1)&gt;g(3-x) .~~~~~~~~~<\/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>10. f(x)  \u4e3a\u5b9a\u4e49\u5728  \\mathbf{R}  \u4e0a\u7684\u53ef\u5bfc\u51fd\u6570, \u4e14  f^{\\prime}(x)&gt;f(x) , \u5bf9\u4efb\u610f\u6b63\u5b9e\u6570  a , \u4e0b\u5217\u5f0f\u5b50\u4e00\u5b9a\u6210\u7acb~~\\\\\u7684\u662f(~~ )~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.  f(a)&lt;\\mathrm{e}^{a} f(0)\n\n\\text~~~ { B. } f(a)&gt;\\mathrm{e}^{a} f(0)~~~\n\nC.  f(a)&lt;\\frac{f(0)}{\\mathrm{e}^{a}} \n~~~D.  f(a)&gt;\\frac{f(0)}{\\mathrm{e}^{a}} \n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/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:B;\n\u63d0\u793a\uff1a\u6784\u9020\u51fd\u6570 g(x)=\\frac{f(x)}{\\mathrm{e}^{x}}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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>11.\\forall   x \\in(0, \\pi) , \u6709  f^{\\prime}(x) \\sin x&gt;f(x) \\cos x , \u8bbe  a=2 f\\left(\\frac{\\pi}{6}\\right), b=\\sqrt{2} f\\left(\\frac{\\pi}{4}\\right), c=f\\left(\\frac{\\pi}{2}\\right) ,~~~~\\\\\u5219  a, b, c  \u7684\u5927\u5c0f\u5173\u7cfb\u4e3a    .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/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 a&lt; b&lt; c \uff1b\u63d0\u793a\uff1a \u6784\u9020\u51fd\u6570  F(x)=\\frac{f(x)}{\\sin x} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n \n","protected":false},"excerpt":{"rendered":"<p>\u6839\u636e\u5bfc\u6570\u5173\u7cfb\u5f0f\u6784\u9020\u51fd\u6570<\/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":[42],"class_list":["post-1502","post","type-post","status-publish","format-standard","hentry","category-4","tag-42"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1502","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=1502"}],"version-history":[{"count":0,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1502\/revisions"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1502"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1502"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1502"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}