What is the extreme f(x,y)=sqrt(1-x^2)+sqrt(1-y^2) ?

The extreme f(x,y)=sqrt(1-x^2)+sqrt(1-y^2) is Maximum(0,0)

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extreme f(x,y)=sqrt(1-x^2)+sqrt(1-y^2)

extreme points

f (x, y) = 1 - x^{2} + 1 - y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - \frac{- x ^{2} + 1 - y ^{2} + 1}{( y ^{2} - 1 ) ( - x ^{2} + 1 ) ^{2} ( - y ^{2} + 1 )}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

- x e^{- \frac{x}{4}}

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

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

f (x) = \frac{7 x}{x - 4}

21 x^{5} + 35 x^{4}

What is the extreme f(x,y)=sqrt(1-x^2)+sqrt(1-y^2) ?
The extreme f(x,y)=sqrt(1-x^2)+sqrt(1-y^2) is Maximum(0,0)