Answer
Images: global and zoomed-in views.
Local maximum: $0.19$ at $x=-0.77$
Local minimum: $-0.19$ at $x=0.77$
$f$ is increasing on: $(-2,-0.77)$ and $(0.77,2)$ ;
$f$ is decreasing on: $(-0.77,0.77)$
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.