{"id":1273,"date":"2023-12-25T21:12:59","date_gmt":"2023-12-25T13:12:59","guid":{"rendered":"http:\/\/www.forillusion.com\/?p=1273"},"modified":"2025-02-14T11:39:10","modified_gmt":"2025-02-14T03:39:10","slug":"differential-mean-value-theorem-and-its-application-word-list","status":"publish","type":"post","link":"https:\/\/www.forillusion.com\/index.php\/differential-mean-value-theorem-and-its-application-word-list\/","title":{"rendered":"\u7b2c\u56db\u7ae0 \u5fae\u5206\u4e2d\u503c\u5b9a\u7406\u53ca\u5176\u5e94\u7528 \u8bcd\u6c47\u8868"},"content":{"rendered":"\n<p><div class=\"has-toc have-toc\"><\/div><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5fae\u5206\u4e2d\u503c\u5b9a\u7406<\/h2>\n\n\n\n<p>\u7f57\u5c14\u5b9a\u7406 Rolle\u2019s theorem<br>\u8d39\u9a6c\u5f15\u7406 Fermat\u2019s lemma<br>\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406 Lagrange\u2019s mean value theorem<br>\u9a7b\u70b9 stationary point<br>\u7a33\u5b9a\u70b9 stable point<br>\u4e34\u754c\u70b9 critical point<br>\u8f85\u52a9\u51fd\u6570 auxiliary function<br>\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u516c\u5f0f Lagrange\u2019s mean value formula<br>\u67ef\u897f\u4e2d\u503c\u5b9a\u7406 Cauchy\u2019s mean value theorem<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6d1b\u5fc5\u8fbe\u6cd5\u5219<\/h2>\n\n\n\n<p>\u6d1b\u5fc5\u8fbe\u6cd5\u5219 L\u2019Hospital\u2019s Rule<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6cf0\u52d2\u516c\u5f0f<\/h2>\n\n\n\n<p>\u4e0d\u5b9a\u5f0f indeterminate form<br>\u6cf0\u52d2\u4e2d\u503c\u5b9a\u7406 Taylor\u2019s mean value theorem<br>\u6cf0\u52d2\u516c\u5f0f Taylor formula<br>\u4f59\u9879 remainder term<br>\u62c9\u683c\u6717\u65e5\u4f59\u9879 Lagrange remainder term<br>\u9ea6\u514b\u52b3\u6797\u516c\u5f0f Maclaurin\u2019s formula<br>n\u9636\u5c40\u90e8\u6cf0\u52d2\u516c\u5f0f local Taylor formula of n-order<br>\u4f69\u4e9a\u8bfa\u516c\u5f0f Peano remainder term<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u51fd\u6570\u7684\u51f8\u6027\u548c\u66f2\u7ebf\u7684\u62d0\u70b9\u3001\u6e10\u8fd1\u7ebf<\/h2>\n\n\n\n<p>\u51f8\u6027 concavity<br>\u4e0a\u51f8 concave upward, cancave up<br>\u4e0b\u51f8(\u51f9) concave downward\u2019 concave down<br>\u62d0\u70b9 inflection point<br>\u51fd\u6570\u7684\u6781\u503c extremum of function<br>\u6781\u5927\u503c local maximum<br>\u6700\u5927\u503c global mximum<br>\u6781\u5c0f\u503c local minimum<br>\u6700\u5c0f\u503c global minimum<br>\u6781\u503c extreme value<br>\u6781\u503c\u70b9 extreme point<br>\u6e10\u8fd1\u7ebf asymptotic line<br>\u659c\u6e10\u8fd1\u7ebf slant asymptote<br>\u6c34\u5e73\u6e10\u8fd1\u7ebf horizontal asymptote<br>\u5782\u76f4\u6e10\u8fd1\u7ebf vertical asymptote<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5fae\u5206\u4e2d\u503c\u5b9a\u7406 \u7f57\u5c14\u5b9a\u7406 Rolle\u2019s theorem\u8d39\u9a6c\u5f15\u7406 Fermat\u2019s lemma\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406 Lagrange\u2019s &#8230;<\/p>","protected":false},"author":1,"featured_media":1275,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[21,19],"class_list":["post-1273","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-20","tag-21","tag-19"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1273","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=1273"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1273\/revisions"}],"predecessor-version":[{"id":1742,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1273\/revisions\/1742"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1275"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1273"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1273"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}