Answer
(a)
Increasing on $(-\infty, \infty)$
(b)
No absolute maximum.
No local maxima.
No absolute minimum.
No local minima.
Work Step by Step
$f$ is defined everywhere.
$ f'(r)=6r^{2}+16,\quad$ defined everywhere.
$f'(r)=0$ for no $r \Rightarrow$ no critical points.
The end behavior of a polynomial is dictated by the leading term,
so f increases from $-\infty$ on the far left to $+\infty$ on the far right.
(a)
Increasing on $(-\infty, \infty)$
Not decreasing anywhere.
(b)
No absolute maximum.
No local maxima.
No absolute minimum.
No local minima.
