What is the extreme f(x,y)=xy-3x-3y-x^2-y^2 ?

The extreme f(x,y)=xy-3x-3y-x^2-y^2 is Maximum(-3,-3)

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extreme f(x,y)=xy-3x-3y-x^2-y^2

extreme points

f (x, y) = x y - 3 x - 3 y - x^{2} - y^{2}

Maximum (- 3, - 3)

Solution steps

Find the critical points:

(- 3, - 3)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- 3, - 3) :

Maximum

Maximum (- 3, - 3)

x^{4} + 3 x y^{3} - x y

F (x, y) = 3 x^{2} y + y^{3} - 3 x^{2} - 3 y^{2} + 2

y = x^{2} + (z - 1)^{2}

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

x^{2} e^{x}

What is the extreme f(x,y)=xy-3x-3y-x^2-y^2 ?
The extreme f(x,y)=xy-3x-3y-x^2-y^2 is Maximum(-3,-3)