What are the critical points of #f(x,y) =x^3 + xy  y^3#?
They are
We need to solve the system
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To find the critical points of ( f(x,y) = x^3 + xy  y^3 ), we need to find where the partial derivatives with respect to ( x ) and ( y ) are both zero.

Partial derivative with respect to ( x ): [ \frac{\partial f}{\partial x} = 3x^2 + y ]

Partial derivative with respect to ( y ): [ \frac{\partial f}{\partial y} = x  3y^2 ]
Setting both partial derivatives equal to zero:
 ( 3x^2 + y = 0 )
 ( x  3y^2 = 0 )
Solve these two equations simultaneously to find the critical points.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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