What is the extreme f(x,y)=sqrt(400-4x^2-25y^2) ?

The extreme f(x,y)=sqrt(400-4x^2-25y^2) is Maximum(0,0)

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extreme f(x,y)=sqrt(400-4x^2-25y^2)

extreme points

f (x, y) = 400 - 4 x^{2} - 25 y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{25 ( 400 - 4 x ^{2} )}{( 400 - 4 x ^{2} - 25 y ^{2} ) 400 - 4 x ^{2} - 25 y ^{2}}

D (x, y) = \frac{40000}{( 400 - 4 x ^{2} - 25 y ^{2} ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

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

f (x) = 10 + 3 x - x^{2}

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

f (x) = \frac{x ^{2} - 11 x + 82}{x - 9}

x^{3} - 12 x^{2} + 45 x + 1

What is the extreme f(x,y)=sqrt(400-4x^2-25y^2) ?
The extreme f(x,y)=sqrt(400-4x^2-25y^2) is Maximum(0,0)