# How do you maximize and minimize #f(x,y)=x^2-y/x# constrained to #0<=x+y<=1#?

There is no upper bound for

The lower bound is

Now, optimize

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To maximize and minimize ( f(x, y) = x^2 - \frac{y}{x} ) constrained to ( 0 \leq x + y \leq 1 ), we need to find critical points and boundary points. Critical points occur where the gradient of ( f(x, y) ) is zero. Boundary points are where ( 0 \leq x + y \leq 1 ). Then, evaluate ( f(x, y) ) at these points and choose 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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