What is the extreme f(x,y)=sqrt(25-5x^2-y^2) ?

The extreme f(x,y)=sqrt(25-5x^2-y^2) is Maximum(0,0)

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extreme f(x,y)=sqrt(25-5x^2-y^2)

extreme points

f (x, y) = 25 - 5 x^{2} - y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{25 - 5 x ^{2}}{( 25 - 5 x ^{2} - y ^{2} ) 25 - 5 x ^{2} - y ^{2}}

D (x, y) = \frac{125}{( - y ^{2} + 25 - 5 x ^{2} ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x) = x^{3} + 3 x y^{2} - 15 x - 12 y

x^{3} - 6 x^{2} + 9 x + 1

x^{4} + y^{4} - 4 x y + 1

f (x) = \frac{x ^{3}}{3} - x^{2} + 1

f (x) = x - 2 + 4 - x

What is the extreme f(x,y)=sqrt(25-5x^2-y^2) ?
The extreme f(x,y)=sqrt(25-5x^2-y^2) is Maximum(0,0)