{"id":4187,"date":"2025-10-13T21:52:00","date_gmt":"2025-10-13T13:52:00","guid":{"rendered":"http:\/\/47.95.222.19\/?p=4187"},"modified":"2025-11-04T16:59:29","modified_gmt":"2025-11-04T08:59:29","slug":"%e5%ae%9e%e9%aa%8c%e5%87%bd%e6%95%b0%e8%a7%a3%e7%ad%94%e9%a2%982","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=4187","title":{"rendered":"\u51fd\u6570\u9898\u76ee2-1"},"content":{"rendered":"\n<figure class=\"wp-block-video\"><video height=\"734\" style=\"aspect-ratio: 1306 \/ 734;\" width=\"1306\" controls src=\"http:\/\/47.95.222.19\/wp-content\/uploads\/2025\/10\/shiyanhanshu2.mp4\"><\/video><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-vivid-cyan-blue-color has-alpha-channel-opacity has-vivid-cyan-blue-background-color has-background is-style-wide\"\/>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-0497fc9f504b71f7cf743c8b8124a61d\">\u9898\u76ee\u5c55\u793a\u2014\u2014\u5148\u63a2\u7a76\u3001\u518d\u542c\u8bb2<\/h5>\n\n\n\n<h5>\u9898\u76ee2<\/h5>\n<p>\u5df2\u77e5\\( f(x) = x\\sin x + a\\cos x \\)\uff0c\\( x = \\pi \\)\u662f\u51fd\u6570\\( g(x) = f'(x) \\)\u7684\u6781\u5c0f\u503c\u70b9\u3002<\/p>\n<p>\uff081\uff09\u6c42\u5b9e\u6570\\( a \\)\u7684\u503c\uff1b<\/p>\n<p>\uff082\uff09\u8ba8\u8bba\u51fd\u6570\\( f(x) \\)\u5728\u533a\u95f4\\((-2\\pi, 2\\pi)\\)\u5185\u7684\u96f6\u70b9\u4e2a\u6570\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color has-medium-font-size wp-elements-2c64de07a9c12d71554b6003f8494698\" style=\"color:#1e4b69;background:linear-gradient(0deg,rgb(230,242,255) 0%,rgb(230,242,255) 16%,rgb(92,175,230) 100%)\">\u89e3\u9898\u63a2\u7a76\u2014\u2014\u70b9\u51fb\u76f4\u8fbe<\/h4>\n\n\n\n\n\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left;\n    background-color: #e6f2ff; \/* \u6de1\u84dd\u8272\u80cc\u666f *\/\n    border: none;\n    padding: 8px 12px;\n    border-radius: 4px;\n    transition: all 0.3s ease; \/* \u5e73\u6ed1\u8fc7\u6e21\u52a8\u753b *\/\n    font-size: 16px;\n  }\n  \n  .video-jump-btn:hover {\n    background-color: #cce0ff; \/* \u7565\u6df1\u7684\u84dd\u8272\u80cc\u666f *\/\n    transform: scale(1.02); \/* \u8f7b\u5fae\u653e\u5927\u6548\u679c *\/\n    box-shadow: 0 2px 4px rgba(0,0,0,0.1); \/* \u589e\u52a0\u8f7b\u5fae\u9634\u5f71 *\/\n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime = 1; document.querySelector('video').play();\">\n\u95ee\u9898(1) \u7b2c\u4e00\u6b65\uff0c\u6839\u636e\\(g'(x)\\)\u6c42\u51fa\\(a = 2\\);\n<\/button>\n\n\n\n<br>\n\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime = 80; document.querySelector('video').play();\">\n    \u7b2c\u4e8c\u6b65\uff1a\u9a8c\u8bc1$a=2$\u65f6\u6ee1\u8db3\u9898\u610f\u3002\n\n<\/button>\n\n\n\n<br>\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime = 140; document.querySelector('video').play();\">\n\u95ee\u9898(2)\n\u7b2c\u4e00\u6b65\uff0c\u5c06\u96f6\u70b9\u4e2a\u6570\u95ee\u9898\u8f6c\u5316\u4e3a\\(\\tan x = -\\displaystyle\\frac{2}{x}\\)\u7684\u4ea4\u70b9\u4e2a\u6570\u95ee\u9898;\n\n<\/button>\n\n\n\n<br>\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime = 378; document.querySelector('video').play();\">\n    \u7b2c\u4e8c\u6b65\uff0c\u753b\u51fa\\(y = \\tan x\\)\u548c\\(y = -\\displaystyle\\frac{2}{x}\\)\u7684\u56fe\u8c61\uff0c\u786e\u5b9a\u51714\u4e2a\u4ea4\u70b9\u3002\n<\/button>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u65b9\u6cd5\u4e00\u3001\u7b54\u6848\u89e3\u6790<\/summary>\n \n\n\n\n<p class=\"mb-2\">\uff081\uff09\\( g(x) = f'(x) = (1 &#8211; a)\\sin x + x\\cos x \\)<\/p>\n        <p class=\"mb-2\">\\( g'(x) = (2 &#8211; a)\\cos x &#8211; x\\sin x \\)<\/p>\n        <p class=\"mb-2\">\u56e0\u4e3a\\( x = \\pi \\)\u662f\\( g(x) \\)\u7684\u6781\u5c0f\u503c\u70b9\uff0c<\/p>\n        <p class=\"mb-2\">\u6240\u4ee5\\( g'(\\pi) = 0 \\)\uff0c\u6240\u4ee5\\( a = 2 \\)<\/p>\n        <p class=\"mb-2\">\u6b64\u65f6\uff0c\\( g'(x) = -x\\sin x \\)<\/p>\n        <p class=\"mb-2\">\u7ecf\u9a8c\u8bc1\uff0c\\( x = \\pi \\)\u662f\\( g(x) \\)\u7684\u6781\u5c0f\u503c\u70b9\u3002<\/p>\n        <p class=\"mb-4\">\u6240\u4ee5\\( a = 2 \\)<\/p>\n\n        <p class=\"mb-2\">\uff082\uff09\\( f(x) = x\\sin x + 2\\cos x \\)\uff0c\\( x \\in (-2\\pi, 2\\pi) \\)<\/p>\n        <p class=\"mb-2\">\u56e0\u4e3a\\( f(-x) = f(x) \\)\uff0c\u6240\u4ee5\\( f(x) \\)\u4e3a\u5076\u51fd\u6570<\/p>\n        <p class=\"mb-2\">\u5148\u8003\u8651\\( x \\in [0, 2\\pi) \\)<\/p>\n      \n        <p class=\"mb-2\">\u5f53\\( x = \\displaystyle\\frac{\\pi}{2} \\)\u6216\\( x = \\displaystyle\\frac{3\\pi}{2} \\)\u65f6\uff0c\\( f(x) \\neq 0 \\)\u3002<\/p>\n        <p class=\"mb-2\">\u5f53\\( x \\neq \\displaystyle\\frac{\\pi}{2} \\)\u4e14\\( x \\neq \\displaystyle\\frac{3\\pi}{2} \\)\u65f6\uff0c<\/p>\n        <p class=\"mb-2\">\u4ee4\\( f(x) = x\\sin x + 2\\cos x = 0 \\)<\/p>\n        <p class=\"mb-2\">\u6240\u4ee5\\( \\tan x = -\\displaystyle\\frac{2}{x} \\)\uff0c\u7531\u56fe\u8c61\u53ef\u77e5\u67092\u4e2a\u4ea4\u70b9\uff0c<\/p>\n        <p class=\"mb-2\">\u6240\u4ee5\\( x \\in (0, 2\\pi) \\)\u65f6\\( f(x) \\)\u67092\u4e2a\u96f6\u70b9\uff0c<\/p>\n        <p class=\"mb-2\">\u56e0\u4e3a\\( f(x) \\)\u4e3a\u5076\u51fd\u6570\uff0c\u6240\u4ee5\\( x \\in (-2\\pi, 0) \\)\u65f6\uff0c\\( f(x) \\)\u67092\u4e2a\u96f6\u70b9<\/p>\n        <p>\u6240\u4ee5\\( f(x) \\)\u5171\u67094\u4e2a\u96f6\u70b9\u3002<\/p>\n<\/details>\n\n\n\n \n","protected":false},"excerpt":{"rendered":"<p>\u9898\u76ee\u5c55\u793a\u2014\u2014\u5148\u63a2\u7a76\u3001\u518d\u542c\u8bb2 \u9898\u76ee2 \u5df2\u77e5\\( f(x) = x\\sin x + a\\cos x \\)\uff0c\\( x [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4187","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4187","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=4187"}],"version-history":[{"count":62,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4187\/revisions"}],"predecessor-version":[{"id":4593,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4187\/revisions\/4593"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4187"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4187"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}