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

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

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

extreme points

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

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

x e^{2 x}

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

f (x) = 3 x^{\frac{2}{3}} + 2 x - 1

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

f (x, y) = \frac{y}{x + y ^{3}}

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