What is the extreme f(x,y)=sqrt(20-x^2-7y^2) ?

The extreme f(x,y)=sqrt(20-x^2-7y^2) is Maximum(0,0)

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extreme f(x,y)=sqrt(20-x^2-7y^2)

extreme points

f (x, y) = 20 - x^{2} - 7 y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{7 ( 20 - x ^{2} )}{( 20 - x ^{2} - 7 y ^{2} ) 20 - x ^{2} - 7 y ^{2}}

D (x, y) = \frac{140}{( - x ^{2} + 20 - 7 y ^{2} ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

y = 3 x^{2} - x - 2

f (x, y) = 4 y^{3} + x^{2} - 12 y^{2} - 36 y + 2

f (0.7) = 17 e^{- \frac{1}{6} x y}

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

f (x, y) = - 11 y^{2} + (x + 16)^{2} + 1

What is the extreme f(x,y)=sqrt(20-x^2-7y^2) ?
The extreme f(x,y)=sqrt(20-x^2-7y^2) is Maximum(0,0)