What is the extreme f(x,y)=sqrt(9-x^2)-sqrt(4-y^2) ?

The extreme f(x,y)=sqrt(9-x^2)-sqrt(4-y^2) is Saddle(0,0)

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extreme f(x,y)=sqrt(9-x^2)-sqrt(4-y^2)

extreme points

f (x, y) = 9 - x^{2} - 4 - y^{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = \frac{36 - x ^{2} + 9 - ( y + 2 ) ( y - 2 )}{( y + 2 ) ( y - 2 ) ( - x ^{2} + 9 ) ^{2} ( - y ^{2} + 4 )}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = x x + 9

f (x) = 6 x^{\frac{2}{3}} - 4 x

f (x) = 3 x^{5} - 4 x^{3}

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

f (x, y) = 4 x^{2} + y^{2} - 8 x + 6 y + 8

What is the extreme f(x,y)=sqrt(9-x^2)-sqrt(4-y^2) ?
The extreme f(x,y)=sqrt(9-x^2)-sqrt(4-y^2) is Saddle(0,0)