What is the extreme f(x,y)=sqrt(121-x^2-y^2) ?

The extreme f(x,y)=sqrt(121-x^2-y^2) is Maximum(0,0)

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extreme f(x,y)=sqrt(121-x^2-y^2)

extreme points

f (x, y) = 121 - x^{2} - y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{121 - x ^{2}}{( 121 - x ^{2} - y ^{2} ) 121 - x ^{2} - y ^{2}}

D (x, y) = \frac{121}{( - x ^{2} - y ^{2} + 121 ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

10 x^{2} + y^{2} - 6 x y - 24 x

f (x, y) = x^{3} - 5 x^{2} + 3 y^{2} + 3 x + 1

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

f (x) = x^{4} + 4 x^{3} + 4 x^{2}

f (x, y) = 100 + x^{2} - y^{2}

What is the extreme f(x,y)=sqrt(121-x^2-y^2) ?
The extreme f(x,y)=sqrt(121-x^2-y^2) is Maximum(0,0)