Answer
local maximum: $5$ at $x=0$
local minimum: $2$ at $x=1$
$f$ is increasing on: $(-1,0)$ and $(2,3)$ ;
$f$ is decreasing on: $(0,2)$
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.