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

The extreme f(x)=2-x^2-xy-y^2 is Maximum(0,0)

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

extreme points

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

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x) = - 2 x^{4} + 20 x^{2} - 18

f (x, y) = - x^{2} - y^{2} + 20 x + 20 y

f (x) = x + \frac{9}{x} + 4, 1 \leq x \leq 18

f (x) = - 2 x + 3 ln (2 x)

f (x, y) = 2 - x + y

What is the extreme f(x)=2-x^2-xy-y^2 ?
The extreme f(x)=2-x^2-xy-y^2 is Maximum(0,0)