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

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As we can see, there are two local maxima at the feasible region frontier. Those results can be achieved using the so called Lagrange Multipliers Method.

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To minimize and maximize ( f(x,y) = \frac{x - y^2}{x + y} ) constrained to ( 0 < xy - y^2 < 5 ):

- Find the critical points of the function inside the constraint region by setting the partial derivatives of ( f(x,y) ) equal to zero and solving for ( x ) and ( y ).
- Use the second partial derivative test to determine whether each critical point corresponds to a maximum, minimum, or saddle point.
- Evaluate the function ( f(x,y) ) at the critical points and at the endpoints of the constraint region to determine the maximum and minimum values.

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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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