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

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

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extreme f(x)=xy-x^2-y^2-2x-2y+4

extreme points

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

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)

y = 3 x - x^{3}

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

f (x) = \frac{x ^{2} - 4}{x ^{2} + 4}, - 4 \leq x \leq 4

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

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

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