Find the absolute maximum and absolute minimum of the function $f(x,y)=xy-5y-25x+125$ on the region above $y=x^2$ and on or below $y=27$.
Critical point: $(5, 25)$
$f$ has a saddle point at $(5, 25)$ so it can't be used to find absolute min/max (correct me if i'm wrong).
Boundary points: $(-5, 0), (5, 0), (0,27)$
$f$ has absolute max of $250$ at $(-5, 0)$
$f$ has absolute min of $-10$ at $(0, 27)$
These are my answers, but the online system (homework portal) doesn't accept them so they may be wrong. Any ideas?