Answer
(a)
Increasing on $(-\infty, -7)\cup(-7,+\infty)$
Not decreasing anywhere.
(b)
No absolute maximum.
No local maxima.
No absolute minimum.
No local minima.
Work Step by Step
$h$ is defined everywhere.
$ h'(r)=3(r+7)^{2},\quad$
which is defined everywhere.
$h'(r)=0$ for no $r=-7 \Rightarrow$ critical point: $r=-7$.
$h(-7)=0$
The end behavior of a polynomial is dictated by the leading term, so $ h(r)\rightarrow -\infty$ on the far left and $ h'(r)\rightarrow +\infty$ on the far right.
Using testpoints in the intervals between critical points,
$h'(-8) \gt 0$
$h'(0) \gt 0$
$ \begin{array}{l}
h':\\
\\
\\
g:\\
\end{array} \quad \begin{array}{ccccccccccc}
-\infty& &-7& &\infty \\
{(} &++ &| &++&) \\ \hline
&\nearrow &0&\nearrow & (+\infty) \\
(-\infty)& & & & \end{array}$
