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\title{Tangente 2}
\range{-5,5}

\real{a = random(-1,1)*randint(1..30)/10}
\real{b = randint(-20..20)/10}
\real{c = randint(-20..20)/10}
\function{f = \a*x^2 + simplify(\b*x) + \c}
\real{x0 = randint(-40..40)/10}
\rational{y0 = evalue(\f, x = \x0)}
\function{df = diff(\f, x)}
\rational{df0 = evalue(\df, x = \x0)}
\function{D = \df0*x-simplify(\df0*\x0 - \y0)}

\integer{xmin = min(-3,\x0-2)}
\integer{xmax = max(3,\x0+2)}
\text{A = slib(function/bounds \f, x, \xmin, \xmax)}
\integer{ymin = min(-3,\A[1]-2)}
\integer{ymax = max(3,\A[2]+2)}
\text{rangex = \xmin,\xmax}
\text{rangey = \ymin,\ymax}
\text{dessin = rangex \rangex
  rangey \rangey
  arrow \xmin,0,\xmax,0,10, black
  arrow 0,\ymin,0,\ymax,10, black
  plot navy,\f
  circle \x0,\y0,5, red
  text black,0,0,roman,0
}
\text{url = draw(200,200
  \dessin)}
\text{dessinc = \dessin
 plot green,\D
}
\text{urlc = draw(200,200
  \dessinc)}

\statement{Donner l'équation de la tangente à la courbe
  d'équation  \(y = \f\) au point  d'abscisse \x0.
  <div class="wimscenter"><img src="\url" alt=""></div>
}
\answer{y=}{\D,x}{type = function}
\text{dessinc = \dessin
 plot green,\D
}
\solution{La droite tangente au point d'abscisse \x0 est dessinée en vert :
    <p class="wimscenter"><img src="\urlc" alt=""></p> }