What is the extreme f(x,y)=sqrt(81-(x^2+y^2)) ?

The extreme f(x,y)=sqrt(81-(x^2+y^2)) is Maximum(0,0)

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extreme f(x,y)=sqrt(81-(x^2+y^2))

extreme points

f (x, y) = 81 - (x^{2} + y^{2})

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{81 - x ^{2}}{( 81 - x ^{2} - y ^{2} ) 81 - x ^{2} - y ^{2}}

D (x, y) = \frac{81}{( - x ^{2} - y ^{2} + 81 ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x) = x^{2} + x y + y^{2} - 12 x + 9

f (x) = 5 + (8 + 5 x)^{\frac{2}{5}}

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

f (x) = x e - 4 x^{2}

e^{x} + \frac{1 - x}{e ^{x}}

What is the extreme f(x,y)=sqrt(81-(x^2+y^2)) ?
The extreme f(x,y)=sqrt(81-(x^2+y^2)) is Maximum(0,0)