3. Let f(r, y)- e (a) Verify that (0, 0) is a critical point. (b) Is this critical point a local maximum, a local minimum or a saddle point? Justify your answer.

Find and classify (local maximum, local minimum, saddle point) all critical points of f(x,y) = x2 - x²y + 2y². Show all supporting work to completely justify your responses.

How do you classify the function f(x, y) = x²y + xy at the origin? This is a local maximum. This is a local minimum. It's impossible to tell. This is not a critical point. This is a saddle point.

Find all the critical points of the function and determine whether each critical point is a local maximum, local minimum, or a saddle point: