{"id":3658,"date":"2024-12-15T22:44:29","date_gmt":"2024-12-15T21:44:29","guid":{"rendered":"https:\/\/mxth.dk\/?p=3658"},"modified":"2026-04-09T22:38:27","modified_gmt":"2026-04-09T20:38:27","slug":"funktionens-tangenthaeldning","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=3658","title":{"rendered":"Funktionens tangenth\u00e6ldning"},"content":{"rendered":"\n

Vi er interesseret i at finde h\u00e6ldningen p\u00e5 tagenten til en funktion i et givet punkt. Til at visualisere processen til at finde h\u00e6ldninge matematisk benyttes GeoGebra til at lave en visuel repr\u00e6sentation. Herunder er en opskrift til, hvad der skal g\u00f8res. Du er selvf\u00f8lgelig velkommen til at pynte mere p\u00e5 det efter eget \u00f8nske om farver og stil.<\/p>\n\n\n

G\u00f8r f\u00f8lgende<\/h2>\n\n
    \n
  1. Indtast en funktion i GeoGebra\u2019s inputfelt<\/li>\n\n\n\n
  2. Opret en skyder ved at indtaste \\(h = 3\\) i inputfeltet<\/li>\n\n\n\n
  3. Indtast et punkt ved at indtaste \\(A = (x, f(x))\\) i inputfeltet. V\u00e6lg en v\u00e6rdi for \\(x\\)<\/li>\n\n\n\n
  4. Indtast endnu et punkt ved at indtaste \\(B = (x+h, f(x+h))\\), hvor x er samme v\u00e6rdi som du valgte for punktet \\(A\\)<\/li>\n\n\n\n
  5. Pr\u00f8v at \u00e6ndre p\u00e5 skyderen<\/li>\n\n\n\n
  6. Lav en ret linje mellem \\(A\\) og \\(B\\)<\/li>\n\n\n\n
  7. Lav en tangent til punktet \\(A\\)<\/li>\n\n\n\n
  8. Hvad sker der, n\u00e5r du \u00e6ndre p\u00e5 skyderen? Hvad sker der n\u00e5r \\(h\\rightarrow 0\\)?<\/li>\n<\/ol>","protected":false},"excerpt":{"rendered":"

    L\u00e6r at finde tangentens h\u00e6ldning til en funktion i et givet punkt ved hj\u00e6lp af GeoGebra. Ved at oprette punkter, en skyder og en tangent, kan du visualisere og udforske, hvordan h\u00e6ldningen \u00e6ndrer sig, n\u00e5r afstanden mellem punkterne mindskes. F\u00f8lg en enkel trinvis guide og oplev, hvad der sker, n\u00e5r h\u21920.<\/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":[11,41,40,3],"tags":[67,74],"class_list":["post-3658","post","type-post","status-publish","format-standard","hentry","category-differentialregning","category-hhx","category-htx","category-matematik","tag-hhx","tag-htx"],"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\/3658","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=3658"}],"version-history":[{"count":2,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3658\/revisions"}],"predecessor-version":[{"id":4310,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3658\/revisions\/4310"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3658"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3658"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}