\documentclass[a4paper]{article}
\usepackage{tkz-tab}
\usepackage{xpatch}

% tkz-tab hardcodes $0$ for the zeros
\xpatchcmd{\tkzTabLine}{$0$}{$\bullet$}{}{}
% we want solid lines
\tikzset{t style/.style={style=solid}}

\begin{document}

\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=2,deltacl=0]
  { /.8, $4(x-1)$ /.8, $3x^{2/3}$ /.8, $f'(x)$ /.8  }
  {,$0$,$1$,} % four main references
\tkzTabLine {,-,t,-,z,+,} % seven denotations
\tkzTabLine {,+,t,+,t,+,}
\tkzTabLine {,-,t,-,z,+,}
\end{tikzpicture}

\end{document}