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

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

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

extreme points

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

Maximum (2, - 2)

Solution steps

Find the critical points:

(2, - 2)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(2, - 2) :

Maximum

Maximum (2, - 2)

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