$f(x)$ will be increasing where $f^\prime(x)$ is positive, and vice versa.
$f(x)$ will be concave up where $f^\prime(x)$ has positive slopes, and vice versa.

Local max at $x =-1$; $f^\prime(x)$ changes from positive to negative.
Inflection points at $x = -0.5$, $0$, $0.5$; $f^\prime(x)$ changes slope.
Local min at $x = 1$; $f^\prime(x)$ changes from negative to positive.

See the hint in part (a).