Source Latex
du cours de mathématiques
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pdfauthor={Yoann Morel},
pdfsubject={Tangentes � une courbe},
pdftitle={Activit� math�matique: Tangentes � une courbe},
pdfkeywords={Math�matiques, 1S, premi�re, S,
tangente, tangentes}
}
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\newcommand{\TITLE}{Notion de tangente � une courbe}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
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\bgex On consid�re le demi-cercle $\mathcal{C}$ de rayon $1$.
Tracer les tangentes � $\mathcal{C}$ aux points d'abscisse $-0,5$,
$0$ et $0,5$.
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\enex
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La courbe $\Cf$, repr�sentative d'une fonction $f$, est donn�e
ci-dessous.
Construire les tangentes � cette courbe aux points d'abscisses
$-5$; $-4$; $-1$; $0$; $2$, $4$ et $5$.
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\begin{pspicture}(-7,-6.5)(6.5,6.7)
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\psplot[linewidth=1.2pt,plotpoints=500]{-6.4}{6.3}{
x 180 mul 3.1415 div sin
x abs 1.1 exp mul
0.85 mul
1 add
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\enex
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Tracer dans le rep�re suivant l'allure d'une courbe passant par tous
les points $A$, $B$, $C$, $D$, $E$ et $F$.
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\vspace{0.6cm}
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% x 180 mul 3.1415 div 3.1415 mul 4 div cos
% x 7 add 1 exp mul
% 0.5 mul
% 1 add
%}
% Tangente en x=0
%\psplot{-2}{2}{x 2 div 9 2 div add}
\rput(0,4.5){\Large\bf$\tm$}\rput(0.3,4.8){$C$}
% Tangente en x=2
%\psplot{0.2}{4.2}{-9 3.1415 mul 8 div x 2 sub mul 1 add}
\rput(2,1){\Large\bf$\tm$}\rput(2.3,1.3){$D$}
% Tangente en x=4
%\psplot{1}{6}{-0.5 x 4 sub mul -9 2 div add}
\rput(4,-4.5){\Large\bf$\tm$}\rput(4.3,-4.8){$E$}
% Tangente en x=-2
%\psplot{-5}{0.5}{5 3.1415 mul 8 div x 2 add mul 1 add}
\rput(-2,1){\Large\bf$\tm$}\rput(-2.3,1.3){$B$}
% Tangente en x=-4
%\psplot{-6.2}{-1}{-0.5 x 4 add mul -0.5 add}
\rput(-4,-0.5){\Large\bf$\tm$}\rput(-4.4,-0.7){$A$}
% Tangente en x=6
%\psplot{4.2}{7.2}{13 3.1415 mul 8 div x 6 sub mul 1 add}
\rput(6,1){\Large\bf$\tm$}\rput(6.3,0.6){$F$}
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\bgex
Dans le rep�re ci-dessous, les droites
$T_{-4}$, $T_{-2}$, $T_0$, $T_2$, $T_4$ et $T_6$
sont les tangentes � la courbe $\Cf$, repr�sentative d'une fonction
$f$, aux points d'abscisses respectives
$-4$; $-2$; $0$; $2$; $4$; $6$.
Tracer l'allure de $\Cf$.
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%\psplot[linewidth=1.2pt,plotpoints=500]{-6.4}{7.2}{
% x 180 mul 3.1415 div 3.1415 mul 4 div cos
% x 7 add 1 exp mul
% 0.5 mul
% 1 add
%}
% Tangente en x=0
\psplot{-2.5}{2.5}{x 2 div 9 2 div add}
\rput(-2.5,3.6){$T_0$}
% Tangente en x=2
\psplot{0.2}{3.6}{-9 3.1415 mul 8 div x 2 sub mul 1 add}
\rput(0.7,6.7){$T_2$}
% Tangente en x=4
\psplot{0.8}{6.8}{-0.5 x 4 sub mul -9 2 div add}
\rput(6.5,-5.4){$T_{4}$}
% Tangente en x=-2
\psplot{-5}{0.3}{5 3.1415 mul 8 div x 2 add mul 1 add}
\rput(-4.6,-3.3){$T_{\mbox{-}2}$}
% Tangente en x=-4
\psplot{-6.5}{-0.8}{-0.5 x 4 add mul -0.5 add}
\rput(-5.5,0.6){$T_{\mbox{-}4}$}
% Tangente en x=6
\psplot{4.4}{7.2}{13 3.1415 mul 8 div x 6 sub mul 1 add}
\rput(4.9,-6.7){$T_6$}
\end{pspicture}
\enex
\enmp
\end{document}
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