What is the extreme f(x,y)=sqrt(64-x^2-y^2) ?

The extreme f(x,y)=sqrt(64-x^2-y^2) is Maximum(0,0)

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extreme f(x,y)=sqrt(64-x^2-y^2)

extreme points

f (x, y) = 64 - x^{2} - y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{64 - x ^{2}}{( 64 - x ^{2} - y ^{2} ) 64 - x ^{2} - y ^{2}}

D (x, y) = \frac{64}{( - x ^{2} - y ^{2} + 64 ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

What is the extreme f(x,y)=sqrt(64-x^2-y^2) ?
The extreme f(x,y)=sqrt(64-x^2-y^2) is Maximum(0,0)