The reason you can work with instead of is that both these functions have their minimal-maximal points exactly at the same points (proof? It's easy...), so:
, and we get the system of non-linear eq's.:
. Since this last eq. has
no real solutions (sum of positive terms on the left), it must be , and then from the 1st
eq. we get
, whose only real solution is .
I hope now you know how to check whether the critical point we get for our function is a maximal, minimal, saddle point or none of these (it, is a minimum, of course), and thus you get the point on your surface.