# How do you minimize and maximize #f(x,y)=(x-2)^2-(y-3)^2/x# constrained to #0<xy-y^2<5#?

##### 1 Answer

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.

#### Explanation:

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!

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