Question

Find and classify all local min and maxima and saddle points of the function f(x,y)=/3yx^2-3xy^2+36xy

I know there are 3 saddle points and one maxima.

This is what I got:
D=FxxFyy-(Fxy)^2
= 36xy-36(x+y-6)^2

But how do i solve for zero?? Im lost on this one. Please help me figure out these points??

Answer 1

First you'd have to find the local maxima/minima. If you have obtained the (four) points, then you can use the second derivative test to determine if each one is a maximum/minimum or saddle point.

Have you found the critical points?

(Unfortunately the definition of f(x,y) above does not seem to be complete.)

Note:singular: maximum, plural: maxima.

Answer 2

Lucy
I think you are wrong,what I got is much that I can't type ,mayb some social network or video call .