The last part of this problem was confusing me, so any help would be appreciated:
Here's the problem:
For the surface defined by the function F(x,y) = 2(x^2)y - y^2 - 4x^2 + 3y, find and classify all critical points.
So far, I've taken the partial derivatives with respect to x and y and have gotten
4xy-8x for the derivative with respect to x and
2x^2 - 2y + 3 for the derivative with respect to y
From those two equations, I got my critical points (by setting the equations = to 0)
For my critical points, I have (+ the square root of .5, 2) and (- the square root of .5, 2).
What I'm confused about is how to classify the points (meaning whether they are minimum, maximum, saddle points, etc.).