Answer
local maximum: $4$ at $x=-1$
local minimum: $0$ at $x=1$
$f$ is increasing on: $[-2,-1]$ and $[1,2]$ ;
$f$ is decreasing on: $[-1,1]$
Work Step by Step
See image (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.