What is the extreme x^2y^2-x-y ?

The extreme x^2y^2-x-y is Saddle(1/(2^{1/3)}, 1/(\sqrt[3]{2)})

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extreme x^2y^2-x-y

extreme

Saddle (\frac{1}{2 ^{\frac{1}{3}}}, \frac{1}{3 2})

Solution steps

Find the critical points:

(\frac{1}{2 ^{\frac{1}{3}}}, \frac{1}{3 2})

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 x^{2}

D (x, y) = - 12 x^{2} y^{2}

Check the sign of at each critical point

Check critical point

(\frac{1}{2 ^{\frac{1}{3}}}, \frac{1}{3 2}) :

Saddle

Saddle (\frac{1}{2 ^{\frac{1}{3}}}, \frac{1}{3 2})

What is the extreme x^2y^2-x-y ?
The extreme x^2y^2-x-y is Saddle(1/(2^{1/3)}, 1/(\sqrt[3]{2)})