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

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

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

extreme points

g (x, y) = 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) = \frac{x ^{2}}{x ^{2} - 1}

f (x) = 5 - 2 x + 3 x^{2} - x^{3}

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

f (x, y) = ln (x + y)

f (x) = - (x + 4)^{3}

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