source: pyromaths/trunk/fuentes/data/ex/lycee/tests/Fd1Tangentes.0.answer @ 423

Last change on this file since 423 was 423, checked in by mabarracus, 4 years ago

add sources from pyromaths 15.10

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1\exercice*
2\begin{enumerate}
3\item  On lit graphiquement le coefficient directeur de chacune des tangentes en ces points.\par
4$f'\,(-4)=4 \qquad f'\,(0)=\dfrac{-3}{2} \qquad f'\,(4)=0$.
5\item
6\begin{asy}[height=6.5cm]
7import graph;
8import interpolate;
9import geometry;
10defaultpen(fontsize(9pt));
11real[] xpt={-6.1,-5,-1,01,05,6.1};
12real[] ypt={02,-2,00,03,-2,-3};
13real[] dy= {00,03,-2,0.75,00,00};
14real f(real t){return pwhermite(xpt,ypt,dy)(t);}
15path Cf=graph(f,-6.1,6.1);
16void tangente(int k,real lg=sqrt(1+dy[k]^2),real ld=lg, pen p=black+1, arrowbar arr=Arrows(SimpleHead,size=9pt)) {
17draw(((xpt[k],ypt[k])-lg*unit((1,dy[k])))--((xpt[k],ypt[k])+ld*unit((1,dy[k]))),p,arr);
18dot((xpt[k],ypt[k]));
19}
20xlimits(-6.1, 6.1);
21ylimits(-5.5, 5.5, Crop);
22xaxis(axis=BottomTop, p=invisible,
23ticks=Ticks(format="%", Step=1, extend=true,
24pTick=gray+.5pt, ptick=dotted)
25);
26yaxis(axis=LeftRight, p=invisible,
27ticks=Ticks(format="%", Step=1, extend=true,
28pTick=gray+.5pt, ptick=dotted)
29);
30xequals(L="$y$", 0, extend=false, arrow=Arrow(HookHead, size=9pt), p=black+1,
31ticks=Ticks(scale(.7)*Label(filltype=Fill(white)), Step=1, Size=3pt,
32end=false, endlabel=false, beginlabel=false, NoZero));
33yequals(L="$x$", 0, extend=false, arrow=Arrow(HookHead, size=9pt), p=black+1,
34ticks=Ticks(scale(.7)*Label(filltype=Fill(white)), Step=1, Size=3pt,
35end=false, endlabel=false, beginlabel=false, NoZero));
36labelx(L=scale(.7)*"$0$", (0,0), align=SW);
37label("$\mathcal C_f$", (-6, f(-6)), 1.5NE, brown);
38draw(Cf, brown+1);
39tangente(1,lg=sqrt(10));
40tangente(2,lg=sqrt(5));
41tangente(3,lg=sqrt(25));
42tangente(4,lg=sqrt(1));
43xlimits(-6.1, 6.1, Crop);
44ylimits(-5.5, 5.5, Crop);
45\end{asy}
46\end{enumerate}
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