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recently I've been trying to create a first and second derivative test showing critical points and increase/decrease/concavity. I've gone this far:

\usepackage{tkz-tab}

\begin{document}

 \begin{figure} 

 \centering 

\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=1]{
    $x$         /1,
    $f'(x)$    /1,
    $f''(x)$   /1
}% 
{
    \hspace{0.2cm}, $0$ , \hspace{0.2cm} 
}%

\tkzTabLine{  , , t , , }

\draw[black,shorten >= 7pt,shorten <= 7pt] 
  ( $(T11)!0.2!(T12)$ ) to[out=-50,in=230,looseness=1.4] ( $(N21)!0.2!(N22)$ );
\draw[black,yscale=-1,shorten >= 7pt,shorten <= 7pt] 
  ( $(N22)!0.1!(N21)$ ) to[out=-50,in=230,looseness=1.4] ( $(T22)!0.1!(T21)$ );
\end{tikzpicture}
\caption{Function Analysis}
\end{figure}

I would like to move the concavity test to the line below and, on the first derivative test line, insert arrows pointing up or down. How can I achieve that?

Thank you,

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