\documentclass{standalone}
\standaloneconfig{border=2mm 2mm 2mm 2mm}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}[scale=1.00]
    \node[] at (2,5) {tableau des variations avec tikz};
    \node[] at (2,4.5) {à utilisser jusqu'à trouver mieux};
    \node[] at (2,4) {ça prend un peu de temps la première fois};
    \draw[thick] (0,3) -- (6,3);%horizontal line
    \draw[thick] (0,0.5) -- (6,0.5);%horizontal line
    \draw[thick] (1,0.5) -- (1,3.4);%vetical line
    \draw[thick] (6,0.5) -- (6,3.4);%vetical line
    \node at (0.5,3.2) {$x$};
    \node at (1.5,3.2) {$-\infty$};
    \node at (2.5,3.2) {$-2$};
    \node at (4.5,3.2) {$1$};
    \node at (5.5,3.2) {$+\infty$};
    \draw[thick] (0,2) -- (6,2);
    \node at (0.5,2.5) {$f'(x)$};
    \node at (0.5,1.3) {$f(x)$};
    \node at (1.8,2.5) {$-$};
    \node at (4.5,2.5) {$0$};
    \node at (3.6,2.5) {$-$};
    \node at (5.3,2.5) {$+$};
    \draw[thick] (2.55,0.5) -- (2.55,3);
    \draw[thick] (2.65,0.5) -- (2.65,3);
    \draw[thick] (4.5,2) -- (4.5,3);
    \draw[dashed, thick] (4.5,0.9) -- (4.5,2);
    %arrows
    \draw[->,thick] (1.2,1.8) -- (2.3,0.7);
    \draw[->,thick] (2.8,1.8) -- (4.3,0.7);
    \draw[->,thick] (4.8,0.7) -- (5.8,1.8);
    \begin{scriptsize}
        \node at (1.35,1.9) {$+\infty$};
        \node at (2.25,0.6) {$-\infty$};
        \node at (2.95,1.9) {$-\infty$};
        \node at (4.5,0.7) {$\sqrt2$};
        \node at (5.7,1.9) {$+\infty$};
    \end{scriptsize}
\end{tikzpicture}

\end{document}