What is the extreme f(x,y)=8-2x^2-2y^2 ?

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

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extreme f(x,y)=8-2x^2-2y^2

extreme points

f (x, y) = 8 - 2 x^{2} - 2 y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = 16

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

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