{"id":1034,"date":"2015-02-06T11:00:46","date_gmt":"2015-02-06T10:00:46","guid":{"rendered":"http:\/\/www.unimath.fr\/?p=1034"},"modified":"2015-02-06T11:03:53","modified_gmt":"2015-02-06T10:03:53","slug":"dm-guide-1s-derivation-n1","status":"publish","type":"post","link":"http:\/\/www.unimath.fr\/?p=1034","title":{"rendered":"DM guid\u00e9 1S – D\u00e9rivation n\u00b01"},"content":{"rendered":"

Sujet :\u00a0Cliquer ici<\/a><\/strong><\/p>\n

    \n
  1. Calcul de\u00a0la d\u00e9riv\u00e9e
    \n[peekaboo_link name=\u00a0\u00bbquestion1″]R\u00e9ponse[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1″] f'(x)=3x^2-4x+1[\/peekaboo_content]<\/li>\n
  2. Recherche des tangentes horizontales
    \n[peekaboo_link name=\u00a0\u00bbquestion2″]Aide 1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion2″] La tangente \u00e0 la courbe de f au point d’abscisse\u00a0x a pour coefficient directeur f'(x)[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion3″]Aide 2[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion3″]Une droite est horizontale si seulement si son coefficient directeur est nul[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion5″]R\u00e9ponse\u00a0\u00a0[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion5″]\u00a0 On trouve x=1 et x=\\frac{1}{3} donc il y a deux points o\u00f9 la tangente est horizontale[\/peekaboo_content]<\/li>\n
  3. a. Equation de la tangente au point A d’abscisse 0
    \n[peekaboo_link name=\u00a0\u00bbquestion6″]Aide[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion6″] \u00a0y=f'(0)(x-0)+f(0)[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion8″]R\u00e9ponse [\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion8″]\u00a0 L’\u00e9quation de la tangente est y=x+1 [\/peekaboo_content]
    \nb.\u00a0Position de la tangente par rapport \u00e0 la courbe de f
    \n[peekaboo_link name=\u00a0\u00bbquestion9″]Aide1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion9″]Si \u00a0f(x) > g(x) sur un intervalle alors la courbe de f est au-dessus de la courbe de g sur cet intervalle[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion10″]Aide2[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion10″] Chercher le signe de f(x)-g(x) c’est-\u00e0-dire de f(x)-(x+1)[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion11″]Aide 3[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion11″]\u00a0f(x)-(x+1)=x^3-2x^2. Factoriser x^2 pour trouver le signe \u00a0[\/peekaboo_content]<\/li>\n
  4. Montrer qu’il existe une unique tangente parall\u00e8le \u00e0 la droite \\Delta ,
    \n[peekaboo_link name=\u00a0\u00bbquestion12″]Aide 1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion12″]\u00a0Deux droites\u00a0sont parall\u00e8les si et seulement si elles ont le m\u00eame coefficient directeur[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion13″]Aide 2[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion13″]\u00a0Le coefficient directeur\u00a0de la tangente au point d’abscisse x est f'(x)\u00a0[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion14″]Aide\u00a03 [\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion14″] On r\u00e9sout f'(x)=\\frac{-1}{3} [\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion15″]Aide 4[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion15″]On doit donc r\u00e9soudre 3x^2-4x+\\frac{4}{3}=0 [\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion16″]R\u00e9ponse[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion16″]Cette \u00e9quation n’a qu’une solution et donc il existe une seule tangente parall\u00e8le \u00e0 la droite \\Delta[\/peekaboo_content]<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Sujet :\u00a0Cliquer ici Calcul de\u00a0la d\u00e9riv\u00e9e [peekaboo_link name=\u00a0\u00bbquestion1″]R\u00e9ponse[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1″] [\/peekaboo_content] Recherche des tangentes horizontales [peekaboo_link name=\u00a0\u00bbquestion2″]Aide 1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion2″] La tangente \u00e0 la courbe de f au point d’abscisse\u00a0x a pour coefficient directeur f'(x)[\/peekaboo_content] [peekaboo_link name=\u00a0\u00bbquestion3″]Aide 2[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion3″]Une droite est horizontale si seulement si son coefficient directeur est nul[\/peekaboo_content] [peekaboo_link name=\u00a0\u00bbquestion5″]R\u00e9ponse\u00a0\u00a0[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion5″]\u00a0 On trouve et donc […]<\/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\/1034"}],"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=1034"}],"version-history":[{"count":14,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts\/1034\/revisions"}],"predecessor-version":[{"id":1052,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts\/1034\/revisions\/1052"}],"wp:attachment":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1034"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}