How do you minimize and maximize #f(x,y)=(x-2)^2-(y-3)^2/x# constrained to #0<xy-y^2<5#?
There are no maxima or minima of f, and no critical points on the set in question. There is only a saddle point and that's not in the constraint region.
The problem is that your constraint region is an open set , meaning it doesn't contain its boundary. Any constrained max and min is either at a critical point of f, on a constraint curve, or on the boundary of a constraint region.
There is a critical point of f at
If instead you meant
Hope this helps!
// dansmath strikes again! \\