# 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.

Hope this helps! // dansmath strikes again! \

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To minimize and maximize ( f(x,y) = \frac{{(x-2)^2 - (y-3)^2}}{{x}} ) constrained to ( 0 < xy - y^2 < 5 ), you first need to find the critical points of ( f(x,y) ) within the given constraint. Then, evaluate ( f(x,y) ) at these critical points as well as at the boundary points of the constraint region to determine the minimum and maximum values of ( f(x,y) ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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