What is the extreme f(x,y)=sqrt(1-(x^2)/4-(y^2)/4) ?

The extreme f(x,y)=sqrt(1-(x^2)/4-(y^2)/4) is Maximum(0,0)

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extreme f(x,y)=sqrt(1-(x^2)/4-(y^2)/4)

extreme points

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

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = \frac{1}{( 4 - x ^{2} - y ^{2} ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x) = x^{3} - 3 x^{2} - 24 x + 32

f (x, y) = 1 - 9 x^{2} - y^{2}

f (x) = x + cos (2 x)

f (x) = 4 x^{3} - 3 x^{2} - 6 x + 3, 0 \leq x \leq 10

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

What is the extreme f(x,y)=sqrt(1-(x^2)/4-(y^2)/4) ?
The extreme f(x,y)=sqrt(1-(x^2)/4-(y^2)/4) is Maximum(0,0)