What is the extreme f(x,y)=sqrt(400-9x^2-36y^2) ?

The extreme f(x,y)=sqrt(400-9x^2-36y^2) is Maximum(0,0)

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extreme f(x,y)=sqrt(400-9x^2-36y^2)

extreme points

f (x, y) = 400 - 9 x^{2} - 36 y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{36 ( 400 - 9 x ^{2} )}{( 400 - 9 x ^{2} - 36 y ^{2} ) 400 - 9 x ^{2} - 36 y ^{2}}

D (x, y) = \frac{129600}{( 400 - 9 x ^{2} - 36 y ^{2} ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x, y) = \frac{1}{3} x^{3} - x

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

f (x) = (x^{2} - 1)^{3}, - 1 \leq x \leq 6

f (x) = (x^{2} - 1)^{3}, - 1 \leq x \leq 4

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

What is the extreme f(x,y)=sqrt(400-9x^2-36y^2) ?
The extreme f(x,y)=sqrt(400-9x^2-36y^2) is Maximum(0,0)