What is the extreme f(x,y)=xy^2-16x^2-2y^2 ?

The extreme f(x,y)=xy^2-16x^2-2y^2 is Maximum(0,0),Saddle(2,8),Saddle(2,-8)

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extreme f(x,y)=xy^2-16x^2-2y^2

extreme points

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

Maximum (0, 0), Saddle (2, 8), Saddle (2, - 8)

Solution steps

Find the critical points:

(0, 0), (2, 8), (2, - 8)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 x - 4

D (x, y) = - 32 (2 x - 4) - 4 y^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(2, 8) :

Saddle

Check critical point

(2, - 8) :

Saddle

Maximum (0, 0), Saddle (2, 8), Saddle (2, - 8)

What is the extreme f(x,y)=xy^2-16x^2-2y^2 ?
The extreme f(x,y)=xy^2-16x^2-2y^2 is Maximum(0,0),Saddle(2,8),Saddle(2,-8)