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 points

f (x, y) = 4 x^{2} y - 2 x - y^{2}

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})

f (x) = \frac{x ^{5} - 5 x}{5}

f (x) = (x - 3) (x + 1) (x + 5)

f (x) = 3 - x^{2}

f (x) = 3 x^{2} - 7 x + 2

x^{2} - 2 x + 9

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)