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Feat: ajout exercices pour tracer et la notion de corde

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This commit is contained in:
Bertrand Benjamin
2022-11-14 08:20:44 +01:00
parent 087d3df807
commit ddbd6a8cbf
6 changed files with 75 additions and 11 deletions
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65
1ST/03_Nombre_derive_et_tangente/exercises.tex
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@@ -262,6 +262,61 @@
\end{tikzpicture}
\end{enumerate}
\end{multicols}
\begin{enumerate}
\setcounter{enumi}{2}
\item
Tracer une courbe qui respecte les points et les tangentes représentées dans les graphiques suivants.
\pgfkeys{tikz/.cd,
tangent length/.store in=\TangentLength,
tangent length=7mm
}
\tikzset{tangent/.style={black,thick},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {\draw[tangent] (-\TangentLength,0) -- (\TangentLength,0);
\fill[tangent] (0,0) circle (2pt);}}}},
}
\begin{tikzpicture}[scale=1]
% Axes
\draw [-latex] (-0.5,0) -- (8,0) node [above] {$x$};
\draw [-latex] (0,-0.5) -- (0,4) node [right] {$y$};
% Origin
\node at (0,0) [below left] {$0$};
% Points
\coordinate (start) at (0,-0.8);
\coordinate (c1) at (3,3);
\coordinate (c2) at (5,1.5);
\coordinate (c3) at (6,4);
\coordinate (end) at (8,2);
% show the points
% \foreach \n in {start,c1,c2,c3,end} \fill [black] (\n)
% circle (2pt) node [below] {};
% join the coordinates
\path [tangent at/.list={0.15,0.3,...,1}] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
\end{tikzpicture}
\hfill
\begin{tikzpicture}[scale=1]
% Axes
\draw [-latex] (-4,0) -- (4,0) node [above] {$x$};
\draw [-latex] (0,-3) -- (0,3) node [right] {$y$};
% Origin
\node at (0,0) [below left] {$0$};
% Points
\coordinate (start) at (-4,-1);
\coordinate (c1) at (-2,3);
\coordinate (c2) at (0,1);
\coordinate (c3) at (2,-2);
\coordinate (end) at (4,0);
% show the points
% \foreach \n in {start,c1,c2,c3,end} \fill [black] (\n)
% circle (2pt) node [below] {};
% join the coordinates
\path [tangent at/.list={0.2,0.4,...,1}] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
\end{tikzpicture}
\end{enumerate}
\end{exercise}
% Nombre dérivé et tangente
@@ -282,7 +337,7 @@
ytick distance=1,
]
\addplot[domain=-4:2,samples=20, color=red, very thick]{0.1*(x+1)^3 + 1};
\addplot [black, mark=*, very thick, only marks] coordinates {(3,1)};
\addplot [black, mark=*, very thick, only marks] coordinates {(1,1)};
\addplot [black, mark=*, very thick, only marks] coordinates {(1,5)};
\addplot [black, mark=*, very thick, only marks] coordinates {(4,2)};
\end{axis}
@@ -297,12 +352,10 @@
xtick distance=1,
ylabel = {$f(x)$},
ytick distance=1,
ymin = -6,
ymax = 6,
]
\addplot[domain=-2:2,samples=50, color=red, very thick]{sin(deg(x*pi/2))*5};
\addplot [black, mark=*, very thick, only marks] coordinates {(-1,-5)};
\addplot [black, mark=*, very thick, only marks] coordinates {(1.5,5*sin(deg(1.5*pi/2)))};
\addplot[domain=-2:2,samples=50, color=red, very thick]{sin(deg(x*pi/2))*2};
\addplot [black, mark=*, very thick, only marks] coordinates {(-1,-2)};
\addplot [black, mark=*, very thick, only marks] coordinates {(1.5,2*sin(deg(1.5*pi/2)))};
\addplot [black, mark=*, very thick, only marks] coordinates {(0,0)};
\end{axis}
\end{tikzpicture}