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\title{Tangente 2}
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\range{-5,5}
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\real{a = random(-1,1)*randint(1..30)/10}
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\real{b = randint(-20..20)/10}
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\real{c = randint(-20..20)/10}
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\function{f = \a*x^2 + simplify(\b*x) + \c}
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\real{x0 = randint(-40..40)/10}
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\rational{y0 = evalue(\f, x = \x0)}
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\function{df = diff(\f, x)}
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\rational{df0 = evalue(\df, x = \x0)}
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\function{D = \df0*x-simplify(\df0*\x0 - \y0)}
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\integer{xmin = min(-3,\x0-2)}
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\integer{xmax = max(3,\x0+2)}
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\text{A = slib(function/bounds \f, x, \xmin, \xmax)}
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\integer{ymin = min(-3,\A[1]-2)}
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\integer{ymax = max(3,\A[2]+2)}
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\text{rangex = \xmin,\xmax}
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\text{rangey = \ymin,\ymax}
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\text{dessin = rangex \rangex
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  rangey \rangey
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  arrow \xmin,0,\xmax,0,10, black
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  arrow 0,\ymin,0,\ymax,10, black
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  plot navy,\f
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  circle \x0,\y0,5, red
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  text black,0,0,roman,0
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}
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\text{url = draw(200,200
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  \dessin)}
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\text{dessinc = \dessin
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 plot green,\D
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}
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\text{urlc = draw(200,200
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  \dessinc)}
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\statement{Donner l'équation de la tangente à la courbe
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  d'équation  \(y = \f\) au point  d'abscisse \x0.
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  <div class="wimscenter"><img src="\url" alt=""></div>
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}
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\answer{y=}{\D,x}{type = function}
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\text{dessinc = \dessin
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 plot green,\D
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}
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\solution{La droite tangente au point d'abscisse \x0 est dessinée en vert :
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    <p class="wimscenter"><img src="\urlc" alt=""></p> }