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 Maximum(0,0)

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

extreme

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

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 Maximum(0,0)