Making a Table (Matrix) with Tikz

I need to get start with making a matrix in Tikz. I need to study the manual but need some help with an example to get started. My minimal example is very poor but it is the best I can do without hours of study

I want to go from:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{shapes.arrows,matrix,positioning}
\usetikzlibrary{decorations.markings}
%%%

\begin{document}
\begin{center}
\begin{tikzpicture}
\matrix[matrix of math nodes,nodes={align=center,inner sep=3pt,
text height=1.5ex,text depth=.25ex,draw=gray!40,ultra thin},draw,inner
sep=0pt,ampersand replacement=\&] (mat1)
at (0,0){
|[fill=green!40!gray,text width=30mm]| \text{Graph over the} \& |
[fill=green!40!gray,text width=11mm]| f(x) \\
|[fill=green!40!gray,text width=30mm]| \text{interval $(a,b)$} \& |
[fill=green!40!gray,text width=11mm]| f(x) \\
|[text width=30mm]|                        \& |[text width=11mm]|   \\
|[text width=30mm]|
\& |[text width=11mm]|  \\
|[text width=30mm]|
\& |[text width=11mm]|  \\
};
\end{tikzpicture}
\end{center}
\end{document}


which outputs:

to a program which outputs:

Again sorry that the minimum example is so weak but I am just getting started with the matrix in TiKz.

• I think a better solution is to insert a tikzpicture in a table. All the other textual parts shoud belong to the table. – Sigur Dec 27 '18 at 18:53

I agree with Sigur's comment that says one should use an ordinary matrix here, color some cells and insert the picture. So this is just for fun, and I stress that I did not even try to simplify it by adding column 1/.style={blabla} and so on. The main reason I am writing this is to advertize Jake's tangents for the picture, and to remind you that, if you want to put a tikzpicture in a node, you should use a \savebox. Further, you can have texts running over two lines in one cell of a matrix.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{matrix}
\usetikzlibrary{decorations.markings}
%%%
\newsavebox\picbox
\sbox\picbox{\begin{tikzpicture}[tangent/.style={ % from https://tex.stackexchange.com/a/25940/121799
decoration={
markings,% switch on markings
mark=
at position #1
with
{
\coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
\coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
\coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
}
},
postaction=decorate
},
use tangent/.style={
shift=(tangent point-#1),
x=(tangent unit vector-#1),
y=(tangent orthogonal unit vector-#1)
},
use tangent/.default=1
]
\draw (-1.5,0) -- (1.5,0);
\draw[red,thick,tangent=0.25,tangent=0.75] plot[domain=-1:1,variable=\x] ({\x},{\x*\x+0.6});
\draw[dashed] (0,0.6) -- (0,0) node[below]{$c$};
\draw [blue, use tangent=1] (-0.6,0) -- (0.6,0) node[midway,below left,draw,inner
sep=-0.4pt,black]{$\times$};
\draw [blue, use tangent=2] (-0.6,0) -- (0.6,0) node[midway,below right,black]{$+$};
\end{tikzpicture}}
\begin{document}
\begin{center}
\begin{tikzpicture}[wide/.style={text width=#1,fill=green!40!gray}]
\matrix[matrix of nodes,nodes={align=center,inner sep=3pt,anchor=center,
ultra thin,draw},draw,inner
sep=0pt,ampersand replacement=\&] (mat1)
at (0,0){
|[wide=30mm]| {\strut Graph over the\\   interval $(a,b)$} \&
|[wide=21mm]| {\strut \\$f(x)$}   \&
|[wide=21mm]| {\strut Sign of $f'(x)$\\ for $x\in]a,c[$} \&
|[wide=21mm]| {\strut Sign of $f'(x)$\\ for $x\in]c,b[$} \&
|[wide=35mm]| {\strut Increasing\\ or decreasing}
\\
|[minimum height=2.7cm]| \usebox\picbox \&
|[text width=21mm,minimum height=2.7cm]| {\strut Relative\\ minimum} \&
|[text width=21mm,minimum height=2.7cm]| {$-$} \&
|[text width=21mm,minimum height=2.7cm]| {$+$} \&
|[text width=35mm,minimum height=2.7cm]| {\strut Decreasing on $]a,c[$;\\ increasing on $]c,b[$}\\
};
\end{tikzpicture}
\end{center}
\end{document}