Subversion Repositories wimsdev

\title{Tangente 3}
\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}
\real{y0 = evalue(\f, x = \x0)}
\function{df = diff(\f,x)}
\real{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)}
\real{x1 = \x0+1}
\real{y1 = \df0*\x1 - \df0*\x0 + \y0}
\text{P0 = slib(draw/convpixel \x0,\y0,200,200,\rangex,\rangey,0,pixels)}
\text{P1 = slib(draw/convpixel \x1,\y1,200,200,\rangex,\rangey,0,pixels)}
\text{rep = \url;line,\P0[1],\P0[2],\P1[1],\P1[2]}

\statement{En utilisant la souris, positionner la  tangente
 à la courbe d'équation \(y = \f\) au point  d'abscisse \x0.
<div class="wims_instruction">
NB : le tracé sera obtenu en définissant deux points
 appartenant à cette tangente.
</div>
<div class="wimscenter">\embed{reply1,200x200}</div>
}
\answer{}{\rep}{type=jsxgraphcurve}

\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>
}