Thread: Having trouble with finding critical points

Hi,

I've just started learning about max & min in two variables. I completely understand the partial derivatives, and how to identify local max/min and saddle points. The only part I don't understand is in the middle, finding the critical points. I know that I'm supposed to set the Partial x and Partial y to zero. But what can I do to find the critical points? I try to solve for one variable in one partial then plug into the second partial to solve for the other. Sometimes, though I check with a graph and my answers don't match. Am I going about this rightly? It seems that I can NEVER find the correct critical points.

You just need to find wherever:

a) both partial derivatives are equal to zero; or
b) either partial derivative does not exist.

Do you maybe have a specific problem with which you'd like some help?