trouble finding critical points on a function, R^2 -> R

Q: Find the local maximum and minimum values and saddle point(s) of the function

I've found the the function's gradiant vector:

but I'm having trouble manipulating these equations to find where . BOB says these points are and , but I'm not sure how to go about proving these are in fact the only points.

Re: trouble finding critical points on a function, R^2 -> R

An exponential is never 0 so you can divide by to get .

Since a vector is 0 if and only if each component is 0, we must have and . And since ab= 0 if and only if either a= 0 or b= 0 we must have x=0, or and y= 0 and . What are the solutions to those equations? ( and **are** solutions but there are two other solutions also.)