is the set of points,
Check for critical points:
Of these 4 points, only 2 belong to , (-1, 2) and (1, 2), for which we have
Now look for extrema along the boundary.
- If
, then
We have 
for 
and 
for 
, which indicates a local maximum at 
and minima at the endpoints of this boundary. So
- If
, then
We have 
for , so we have extrema at the endpoints of this boundary.
- If
, then
which tells us 
is strictly increasing on this boundary, giving the extrema we already know about,
- If
, then
We have 
for 
and 
, and 
for 
. This indicates a maximum at 
and a minimum at 
, with
From this analysis, we find that attains an absolute maximum of 19 at (-1, 2) and (2, 2), and an absolute minimum of -17 at (-2, -2).
