(a) Find the critical point of $f(x,y) = \left(x^{2}-y\right)\!\left(x^{2}+3y\right)$.
$(x,y) =$

(b) Find the discriminant, $D(x,y)$ for the function.
$D(x,y) =$
what is the value of the discriminant at the critical point?
$D =$
What does this tell us about the critical point?
? The critical point is a local maximum The critical point is a local minimum The critical point is a saddle point The discriminant doesn't tell us anything

(c) Sketch contours near the critical point to determine, or confirm, whether it is a local maximum, a local minimum, a saddle point, or none of these.
? The critical point is a local maximum The critical point is a local minimum The critical point is a saddle point The discriminant doesn't tell us anything