What is the extreme f(x,y)=2+sqrt(9-x^2-y^2) ?

The extreme f(x,y)=2+sqrt(9-x^2-y^2) is Maximum(0,0)

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extreme f(x,y)=2+sqrt(9-x^2-y^2)

extreme points

f (x, y) = 2 + 9 - x^{2} - y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{9 - x ^{2}}{( 9 - x ^{2} - y ^{2} ) 9 - x ^{2} - y ^{2}}

D (x, y) = \frac{9}{( - x ^{2} - y ^{2} + 9 ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x) = x^{2} - 5 x + 6

f (x) = x x + 2

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

f (x, y) = 6 - 3 x - 2 y

f (x) = cos (x) + sin (x)

What is the extreme f(x,y)=2+sqrt(9-x^2-y^2) ?
The extreme f(x,y)=2+sqrt(9-x^2-y^2) is Maximum(0,0)