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 $x=-2,0,1$
$(b)$
$\left[\begin{array}{cccccc}
& (-\infty,-2) & (-2,0) & (0,1) & (1,\infty)\\
\text{test point} & -3 & -1 & 0.5 & 2\\
\text{evaluate }f' & 36 & -2 & -0.05 & 1\\
\text{sign of }f' & + & - & - & +\\
\text{behavior of }f(x) & \nearrow^{...} & {}^{...}\searrow & \searrow & \nearrow
\end{array}\right]$
(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 $x=1$
