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

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

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

extreme points

f (x) = x y - 2 x - 2 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) = 3

Check the sign of at each critical point

Check critical point

(- 2, - 2) :

Maximum

Maximum (- 2, - 2)

f (x, y) = 2 x^{3} + x y^{2} + 5 x^{2} + y^{2} + 6

f (x) = x (6 - 2 x)^{2}

f (x, y) = 22 x^{4} + 22 y^{4} - 4 x y + 18

f (x) = \frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} + \frac{2}{3}

f (x, y) = - 4 \cdot \frac{x ^{2} + 6 x + 8}{y ^{2} + 6 y + 6}

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