What is the extreme f(x,y)=4x^2y-2x-y^2 ?

The extreme f(x,y)=4x^2y-2x-y^2 is Saddle(1/2 , 1/2)

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extreme f(x,y)=4x^2y-2x-y^2

extreme

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

Solution steps

Find the critical points:

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

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

D (x, y) = - 16 y - 64 x^{2}

Check the sign of at each critical point

Check critical point

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

Saddle

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

What is the extreme f(x,y)=4x^2y-2x-y^2 ?
The extreme f(x,y)=4x^2y-2x-y^2 is Saddle(1/2 , 1/2)