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

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

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

extreme

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - \frac{x ^{2} + y ^{2} + 64}{( x ^{2} + y ^{2} - 64 ) ^{3}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

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