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\section{Exemples}

Soit à étudier la fonction $g\ :\ x\mapsto 8x^3-4x^2-2x-1$.

Grâce à $g'(x)=2(6x+1)(2x-1)$, on construit aisément le tableau de variations~:

\unitlength=1mm
\begin{picture}(100,55)
%
\put(05,50){\line(1,0){120}}  \put(08,45){x} \put(22,45){$-\infty$} \put(50,45){$-1/6$}
\put(80,45){$+1/2$}           \put(115,45){$+\infty$}
%
\put(05,40){\line(1,0){120}}  \put(08,33){g'(x)} \put(36,33){$+$}
\put(54,33){$0$}              \put(69,33){$-$}   \put(84,33){$0$}
\put(99,33){$+$}
%
\put(05,30){\line(1,0){120}}  \put(22,13){$-\infty$}
\put(48,25){$-22/7$}          \put(82,13){$-2$}
\put(115,25){$+\infty$}       \put(08,20){g(x)}
%
\put(05,10){\line(1,0){120}}  \put(05,10){\line(0,1){40}}
\put(020,10){\line(0,1){40}}  \put(125,10){\line(0,1){40}}
\put(55,10){\line(0,1){13}}% pour 22/7
\put(55,29){\line(0,1){03}}   \put(55,37){\line(0,1){03}}
\put(85,19){\line(0,1){13}}   \put(85,37){\line(0,1){03}}
\put(32,17){\vector(2,1){15}} \put(90,17){\vector(3,1){20}}
\put(61,25){\vector(2,-1){18}}
\end{picture}

D'où le tracé

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