What is the extreme f(x,y)=6-x^2-6x-y^2 ?

The extreme f(x,y)=6-x^2-6x-y^2 is Maximum(-3,0)

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extreme f(x,y)=6-x^2-6x-y^2

extreme points

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

Maximum (- 3, 0)

Solution steps

Find the critical points:

(- 3, 0)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- 3, 0) :

Maximum

Maximum (- 3, 0)

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

y = - 2 x^{2} + 10 x + 1

f (x) = x + cos (x), - 2 π \leq x \leq 2 π

f (x) = 8 - x^{\frac{2}{3}}

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

What is the extreme f(x,y)=6-x^2-6x-y^2 ?
The extreme f(x,y)=6-x^2-6x-y^2 is Maximum(-3,0)