What is the extreme f(x,y)=-5x^2+4xy-y^2+16x+10 ?

The extreme f(x,y)=-5x^2+4xy-y^2+16x+10 is Maximum(8,16)

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extreme f(x,y)=-5x^2+4xy-y^2+16x+10

extreme points

f (x, y) = - 5 x^{2} + 4 x y - y^{2} + 16 x + 10

Maximum (8, 16)

Solution steps

Find the critical points:

(8, 16)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(8, 16) :

Maximum

Maximum (8, 16)

What is the extreme f(x,y)=-5x^2+4xy-y^2+16x+10 ?
The extreme f(x,y)=-5x^2+4xy-y^2+16x+10 is Maximum(8,16)