Vrftsjtryk

I need help a little on the matrix again and putting together the matrix and tikzpicture I created.

documentclass{article}

usepackage{tikz,amsmath}

usetikzlibrary{decorations.pathreplacing} %%% For curly braces

usetikzlibrary{shapes.arrows,matrix,positioning}





begin{document}



The Tikzpicture



begin{center}

begin{tikzpicture}

draw[<->,black,thick] (0,0)--(9,0);

draw (3,2pt)--(3,-2pt) node[below] {textcolor{red}{$-3$}};

draw (6,2pt)--(6,-2pt) node[below] {textcolor{red}{$3$}};

draw[decoration={brace,raise=5pt},decorate]

 (0,0) -- node[above=6pt,align=center] {$(-infty,3)$} (2.95,0);

draw[decoration={brace,raise=5pt},decorate]

 (3.05,0) -- node[above=6pt,align=center] {$(-3,3)$} (5.95,0);

draw[decoration={brace,raise=5pt},decorate]

 (6.05,0) -- node[above=6pt,align=center] {$(3,infty)$} (9,0);

end{tikzpicture}

end{center}



The Matrix



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){

f^{prime}(-4)>0 & f^{prime}(0)<0 & f^{prime}(4)>0  \

 |[text width=33mm,wide=33mm]| {text{Test Value}} & 

|[text width=33mm,minimum height=.5cm]| {$x=-4 $} &

 |[text width=33mm,minimum height=.5cm]| {$x=0$} &

|[text width=33mm,minimum height=.5cm]| {$x=4$} &    \

 |[text width=33mm,wide=33mm]| text{Sign of $f^{prime}(x)$} & 

|[text width=33mm,minimum height=.5cm]| {$f^{prime}(-4)>0$} &

 |[text width=33mm,minimum height=.5cm]| {$f^{prime}(0)<0$} &

|[text width=33mm,minimum height=.5cm]| {$f^{prime}(4)>0$} &    \

|[wide=33mm]| {strut Result\} & 

|[text width=33mm]| {strut $f$ is increasing \ on $(-infty,-3)$} & 

|[text width=33mm]| {strut $f$ is decreasing \ on $(-3,3)$} &

|[text width=33mm]| {strut $f$ is decreasing \ on $(3,infty)$}  & \                       

};

end{tikzpicture}

end{center}



end{document}

This Outputs:

I am trying to put them together like in this (but a different yet similar example):

like this?

i merge both tikzpictures in one. arrow and braces positions are determined relatively to matrix:

documentclass{article}

usepackage{tikz}

usetikzlibrary{arrows.meta,

                decorations.pathreplacing,  % For curly braces

                matrix,

                positioning}

usepackage{amsmath}



begin{document}

    begin{center}

begin{tikzpicture}[

B/.style = {decoration={brace,raise=2mm,amplitude=1mm,

                        pre=moveto,pre length=1pt,

                        post=moveto,post length=1pt},thick, decorate},

arr/.style = {-Straight Barb, red, thick, shorten >=1mm, shorten <=1mm},

box/.style = {fill=white, text width=24mm, align=center, inner sep=0.5mm,

              font=footnotesize, pos=0.25, 

              anchor=center,yshift=-2ex}

                    ]

matrix (m) [matrix of math nodes,

             nodes={thin, draw,

                    text width=28mm, minimum height=4ex, align=center,

                    inner sep=1mm, outer sep=0pt, anchor=center},

             column sep=-pgflinewidth,

                row sep=-pgflinewidth,

             column 1/.style = {nodes={text width=21mm,

                                align=left,fill=olive!50}},

                row 3/.style = {nodes={minimum height=8ex}},

             ]

{

text{Test Value}

    &  x=-4                &  x=0             &  x=4             \

text{Sign of } f^{prime}(x)

    &  f^{prime}(-4)>0    &  f^{prime}(0)<0 &  f^{prime}(4)>0 \

text{Result}

    &  begin{gathered} f text{ is increasing on}\

        (-infty,-3)

        end{gathered}

        &  begin{gathered} f text{ is decreasing on}\

        (-3,3)

        end{gathered}

        &  begin{gathered} f text{ is decreasing on}\

        (3,infty)

        end{gathered}          \

};

coordinate[above=7mm of m-1-1.north]   (aux1);

coordinate[above=1mm of aux1]          (aux2);

draw[Stealth-Stealth,thick] (aux1)  -- (aux1 -| m-1-4.east);

draw (aux2 -| m-1-3.west) -- + (0,-2mm) node[below] {textcolor{red}{$-3$}}

      (aux2 -| m-1-3.east) -- + (0,-2mm) node[below] {textcolor{red}{$3$}};

draw[B]    (aux1) --

    node[above=3mm] {$(-infty,-3)$}

            (aux1 -| m-1-2.east);

draw[B]    (aux1 -| m-1-3.west) --

    node[above=3mm] {$(-3,3)$}

            (aux1 -| m-1-3.east);

draw[B]    (aux1 -| m-1-4.west) --

    node[above=3mm] {$(3,infty)$}

            (aux1 -| m-1-4.east);

draw[arr]

    (m-3-2.south) -- + (0,-0.6) -| ([xshift=-2mm] m-3-3.south)

    node[box] {Change indicates relative maximum at $x=-3$};

draw[arr]

    ([xshift=2mm] m-3-3.south) -- + (0,-0.6) -| (m-3-4.south)

    node[box] {Change indicates relative minimum at $x=3$};

end{tikzpicture}

    end{center}

end{document}

edit: added are red arrows with text (below of the matrix) and defined minimum height for cells in the last matrix's row.