Answer
Local maximum: $3$ at $x=0$
Local minima:
$0.95$ at $x=-1.87$ and $2.65$ at $x=0.97$
$f$ is increasing on: $(-1.87,0)$ and $(0.97,2 )$
$f$ is decreasing on: $(-3,-1.87)$ and $(0,0.97 )$
Work Step by Step
(graphed with desmos.com).
A local maximum at x=c exists if there is an interval around c such that f(c) is the largest function value on that interval.
A local minimum at x=c exists if there is an interval around c such that f(c) is the lowest function value on that interval.