{"id":97,"date":"2020-01-11T20:33:19","date_gmt":"2020-01-11T20:33:19","guid":{"rendered":"https:\/\/henriksenmatematik.wordpress.com\/?p=97"},"modified":"2026-04-09T22:15:16","modified_gmt":"2026-04-09T20:15:16","slug":"differentiabilitet","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=97","title":{"rendered":"Differentiabilitet"},"content":{"rendered":"\n<blockquote><h3>Definition<\/h3><p>  <strong>differentiabilitet,<\/strong> (af lat.), det at kunne differentieres<\/p><p>  denstoredanske.dk\n<\/p><\/blockquote>\n\n\n\n<p>En funktion <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=f%28x%29&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"f(x)\" class=\"latex\" \/> siges at v\u00e6re differentiabel i et interval <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Ba%3B+b%5D&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"[a; b]\" class=\"latex\" \/>, n\u00e5r den genneml\u00f8ber hele intervallet i bl\u00f8de kurver, det vil sige at det ikke kn\u00e6kker.<\/p>\n\n\n\n<p>Et eksempel p\u00e5 en differentiabel funktion kunne for eksempel v\u00e6re<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.dropbox.com\/s\/o2h5nj7jg4jsoa2\/img-web%20%284%29.png?raw=1\" alt=\"Differentiabel funktion\" width=\"503\" height=\"512\" \/><\/figure>\n\n\n\n<p>Det ses her, at funktionen i hele definitionsintervallet har bl\u00f8de kurver og derfor er differentiabel.<\/p>\n\n\n\n<p>Et eksempel p\u00e5 en <strong>ikke<\/strong> differentiabel funktion kunne v\u00e6re<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.dropbox.com\/s\/roegwdsodhomkpa\/img-web%20%283%29.png?raw=1\" alt=\"Ikke differnetialbel funktion\" width=\"503\" height=\"512\" \/><\/figure>\n\n\n\n<p>Grunden til at det sidste eksempel er et eksempel p\u00e5 en <strong>ikke<\/strong> differentiabel funktion er, at i punktet hvor funktionen kn\u00e6kker er mulighed for, at der er to l\u00f8sninger til tangenth\u00e6ldningen. Hvis vi v\u00e6lger et punkt P til venstre for kn\u00e6kket, finder tangenten med et tangentv\u00e6rkt\u00f8j i for eksempel GeoGebra s\u00e5 vil tangenten i punktet v\u00e6re anderledes n\u00e5r vil bev\u00e6ger punktet P hen til kn\u00e6kket end hvis vi havde valgt et punkt til h\u00f8jre for kn\u00e6kket.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definition differentiabilitet, (af lat.), det at kunne differentieres denstoredanske.dk En funktion siges at v\u00e6re differentiabel i et interval , n\u00e5r den genneml\u00f8ber hele intervallet i bl\u00f8de kurver, det vil sige at det ikke kn\u00e6kker. Et eksempel p\u00e5 en differentiabel funktion kunne for eksempel v\u00e6re Det ses her, at funktionen i hele definitionsintervallet har bl\u00f8de kurver [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[11,3],"tags":[],"class_list":["post-97","post","type-post","status-publish","format-standard","hentry","category-differentialregning","category-matematik"],"featured_image_src":null,"author_info":{"display_name":"Henriksen","author_link":"https:\/\/mxth.dk\/?author=1"},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/97","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=97"}],"version-history":[{"count":1,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/97\/revisions"}],"predecessor-version":[{"id":4298,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/97\/revisions\/4298"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=97"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=97"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=97"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}