{"id":4024,"date":"2020-05-03T09:49:18","date_gmt":"2020-05-03T08:49:18","guid":{"rendered":"http:\/\/www.unimath.fr\/?p=4024"},"modified":"2020-05-03T11:24:11","modified_gmt":"2020-05-03T10:24:11","slug":"dm-guide-fonction-ln-010520","status":"publish","type":"post","link":"http:\/\/www.unimath.fr\/?p=4024","title":{"rendered":"DM guid\u00e9 Fonction ln 010520"},"content":{"rendered":"

Sujet<\/a><\/strong><\/p>\n

Partie A<\/strong><\/p>\n

    \n
  1. a.<\/strong> [peekaboo_link name=\u00a0\u00bbquestion1a\u00a0\u00bb]Aide pour le calcul de f'(x)[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1a\u00a0\u00bb] Pour d\u00e9river f : utiliser les d\u00e9riv\u00e9es de uv et de ln(u) [\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion1a2″]R\u00e9ponses des d\u00e9riv\u00e9es premi\u00e8re et seconde [\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1a2″] On trouve f'(x)=\\ln\\left(1+\\dfrac{3}{x} \\right)-\\dfrac{3}{x+3}
    \net la d\u00e9riv\u00e9e seconde est : \\dfrac{-3}{x(x+3)} +\\dfrac{3}{(x+3)^2} [\/peekaboo_content]
    \nb.<\/strong> [peekaboo_link name=\u00a0\u00bbquestion1b\u00a0\u00bb]Variation de f'[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1b\u00a0\u00bb] Il faut chercher le signe de la d\u00e9riv\u00e9e seconde.
    \nPour cela, r\u00e9duire la d\u00e9riv\u00e9e seconde au m\u00eame d\u00e9nominateur.
    \nOn trouve une fraction toujours n\u00e9gative. [\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion1b2″]Limite de f'[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1b2″] Reconna\u00eetre la d\u00e9riv\u00e9e d’une compos\u00e9e. A r\u00e9diger avec X.
    \nLa limite est \u00e9gale \u00e0 0[\/peekaboo_content]
    \nc.\u00a0<\/strong>[peekaboo_link name=\u00a0\u00bbquestion1c\u00a0\u00bb]En d\u00e9duire le signe de f'[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1c\u00a0\u00bb] Les variations de f’ et sa limite donne le signe de f’.
    \nRemarque : La limite qui vaut 0 n’est jamais atteinte donc f'(x) est diff\u00e9rent de 0. [\/peekaboo_content]<\/span><\/li>\n<\/ol>\n

    Partie B<\/strong><\/p>\n

      \n
    1. [peekaboo_link name=\u00a0\u00bbquestionB1″]D\u00e9riv\u00e9e de g
      \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionB1″] g'(x)=\\dfrac{9}{(x+3)^2}
      \n[\/peekaboo_content]<\/li>\n
    2. [peekaboo_link name=\u00a0\u00bbquestionB2″]Limite de g
      \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionB2″] Pour lever l’ind\u00e9termination, il faut factoriser x puis simplifier
      \n[\/peekaboo_content]<\/li>\n
    3. [peekaboo_link name=\u00a0\u00bbquestionB3″]R\u00e9ponse pour f(x) – g(x)
      \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionB3″] f(x)-g(x)=xf'(x)
      \n[\/peekaboo_content]<\/li>\n
    4. [peekaboo_link name=\u00a0\u00bbquestionB4″]Interpr\u00e9tation du signe de f(x) – g(x)
      \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionB4″] Le signe de f(x) – g(x) donne une indication sur la position relative des courbes de f et de g
      \n[\/peekaboo_content]<\/li>\n<\/ol>\n

      Partie C<\/strong><\/p>\n

        \n
      1. [peekaboo_link name=\u00a0\u00bbquestionC1″]Equation de la tangente
        \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionC1″] y=\\left(\\ln\\left(1+\\dfrac{3}{a} \\right)-\\dfrac{3}{a+3}\\right)x+ \\dfrac{3a}{a+3}
        \n[\/peekaboo_content]<\/li>\n
      2. [peekaboo_link name=\u00a0\u00bbquestionC2″]Aide pour le point d’intersection avec l’axe (Oy)
        \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionC2″] Un point qui est sur l’axe des ordonn\u00e9es v\u00e9rifie x = 0
        \n[\/peekaboo_content]<\/li>\n
      3. [peekaboo_link name=\u00a0\u00bbquestionC3″]Aide 1 pour la construction de la tangente
        \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionC3″] Pour tracer la tangente, il faut commencer par chercher le point de coordonn\u00e9es (0 ; g(3))
        \n[\/peekaboo_content][peekaboo_link name=\u00a0\u00bbquestionC32″]Aide 2 pour la construction de la tangente
        \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionC32″] g(3) s’obtient \u00e0 partir de la courbe de g.
        \nEn effet si x = 3 alors y = g(3)
        \n[\/peekaboo_content][peekaboo_link name=\u00a0\u00bbquestionC33″]Aide 3 pour la construction de la tangente
        \n[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestionC33″] Pour tracer la tangente on relie le point de coordonn\u00e9es (0 ; g(3)) au point A
        \n[\/peekaboo_content]<\/li>\n<\/ol>\n

         <\/p>\n","protected":false},"excerpt":{"rendered":"

        Sujet Partie A a. [peekaboo_link name=\u00a0\u00bbquestion1a\u00a0\u00bb]Aide pour le calcul de f'(x)[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1a\u00a0\u00bb] Pour d\u00e9river f : utiliser les d\u00e9riv\u00e9es de uv et de ln(u) [\/peekaboo_content] [peekaboo_link name=\u00a0\u00bbquestion1a2″]R\u00e9ponses des d\u00e9riv\u00e9es premi\u00e8re et seconde [\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1a2″] On trouve et la d\u00e9riv\u00e9e seconde est : [\/peekaboo_content] b. [peekaboo_link name=\u00a0\u00bbquestion1b\u00a0\u00bb]Variation de f'[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1b\u00a0\u00bb] Il faut chercher le signe de […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts\/4024"}],"collection":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4024"}],"version-history":[{"count":25,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts\/4024\/revisions"}],"predecessor-version":[{"id":4057,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts\/4024\/revisions\/4057"}],"wp:attachment":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4024"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4024"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4024"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}