2

Is there a way to bring the zero infront of the dashed line? Maybe place in a white background?

\documentclass[]{article}
\usepackage{tkz-tab}
\usepackage{amsmath,amssymb}

\begin{document}

\begin{tikzpicture}
\tikzset{t style/.style = {style = dashed}}
    \tkzTabInit{$x$ /.8 , $f'(x)$ /.8, $f(x)$/.8}{$-\infty$, $0$ , $+\infty$};
    \tkzTabLine{,+,z,-}
    \tkzTabLine{,\nearrow ,t, \searrow }

    \end{tikzpicture}
\end{document}

enter image description here

2

With the help of this post:

\documentclass[]{article}
\usepackage{xpatch}
\usepackage{tkz-tab}
\usepackage{amsmath,amssymb}
\makeatletter
\xpatchcmd{\tkzTabLine}
{\node at (Z\thetkz@cnt@impair\thetkz@cnt@lg){$0$};} % search
{\node[fill=white] at (Z\thetkz@cnt@impair\thetkz@cnt@lg){$0$};} % replace
{}{}
\makeatother
\begin{document}

    \begin{tikzpicture}
    \tikzset{t style/.style = {style = dashed}}
    \tkzTabInit{$x$ /.8 , $f'(x)$ /.8, $f(x)$/.8}{$-\infty$, $0$ , $+\infty$};
    \tkzTabLine{,+,z,-}
    \tkzTabLine{,\nearrow ,t, \searrow }

    \end{tikzpicture}
\end{document}

enter image description here

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