mjhjmtu

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

documentclassarticle
usepackagetikz,amsmath
usetikzlibrarydecorations.pathreplacing %%% For curly braces
usetikzlibraryshapes.arrows,matrix,positioning


begindocument

The Tikzpicture

begincenter
begintikzpicture
draw[<->,black,thick] (0,0)--(9,0);
draw (3,2pt)--(3,-2pt) node[below] textcolorred$-3$;
draw (6,2pt)--(6,-2pt) node[below] textcolorred$3$;
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);
endtikzpicture
endcenter

The Matrix

begincenter
begintikzpicture[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)[text width=33mm,wide=33mm];
endtikzpicture
endcenter

enddocument

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:

documentclassarticle
usepackagetikz
usetikzlibraryarrows.meta,
 decorations.pathreplacing, % For curly braces
 matrix,
 positioning
usepackageamsmath

begindocument
 begincenter
begintikzpicture[
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,
 ]

textTest Value
 & x=-4 & x=0 & x=4 \
textSign of f^prime(x)
 & f^prime(-4)>0 & f^prime(0)<0 & f^prime(4)>0 \
textResult
 & begingathered f text is increasing on\
 (-infty,-3)
 endgathered
 & begingathered f text is decreasing on\
 (-3,3)
 endgathered
 & begingathered f text is decreasing on\
 (3,infty)
 endgathered \
;
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] textcolorred$-3$
 (aux2 -| m-1-3.east) -- + (0,-2mm) node[below] textcolorred$3$;
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 $x=3$;
endtikzpicture
 endcenter
enddocument

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