What is the extreme g(x,y)=sqrt(4-x^{(2))-y^{(2)}} ?

The extreme g(x,y)=sqrt(4-x^{(2))-y^{(2)}} is Maximum(0,0)

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extreme g(x,y)=sqrt(4-x^{(2))-y^{(2)}}

extreme points

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

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

- 2 x^{2} + 200 x

f (x, y) = 3 x - 1.5 x y + 0.5 y^{3}

f (x) = sin (x) \cdot cos (x)

x^{2} + x y + y^{2} + 4 y

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

What is the extreme g(x,y)=sqrt(4-x^{(2))-y^{(2)}} ?
The extreme g(x,y)=sqrt(4-x^{(2))-y^{(2)}} is Maximum(0,0)