Answer
$ a.\quad$ critical points at $x=-2,0,1$
$ b.\quad$ increasing on $(-\infty,-2)\cup(1, \infty)$, decreasing on $(-2,0)\cup(0,1)$.
$ c.\quad$ local minimum at $x=1$
Work Step by Step
$(a)$
$f'$ is defined everywhere except at $ x=-2\qquad$ ... critical point
$f'(x)=0$ for $ x=0,1\qquad$ ... critical points
Critical points at $x=-2,0,1$
$(b)$
$\left[\begin{array}{lllll}
& (-\infty,-2) & (-2,0) & (0,1) & (1,\infty)\\
\text{test point} & -3 & -1 & 0.5 & 2\\
\text{evaluate }f' & 36 & -2 & -0.05 & 1\\
\text{sign of }f' & + & - & - & +\\
\text{behavior of }f(x) & \nearrow^{...} & {}^{...}\searrow & \searrow & \nearrow
\end{array}\right]$
(the "$\nearrow^{... },\ {}^{...}\searrow$" indicate that $f'$ is undefined at the border.)
f is increasing on $(-\infty,-2)\cup(1, \infty)$, decreasing on $(-2,0)\cup(0,1)$.
$(c)$
From the table, we see that f has:
a local minimum at $x=1$,
