What is the extreme f(x,y)=sqrt(6-(x^2)/3-(y^2)/2) ?

The extreme f(x,y)=sqrt(6-(x^2)/3-(y^2)/2) is Maximum(0,0)

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extreme f(x,y)=sqrt(6-(x^2)/3-(y^2)/2)

extreme points

f (x, y) = 6 - \frac{x ^{2}}{3} - \frac{y ^{2}}{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{6 ( 18 - x ^{2} )}{( 36 - 2 x ^{2} - 3 y ^{2} ) 36 - 2 x ^{2} - 3 y ^{2}}

D (x, y) = \frac{36}{( 36 - 2 x ^{2} - 3 y ^{2} ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

What is the extreme f(x,y)=sqrt(6-(x^2)/3-(y^2)/2) ?
The extreme f(x,y)=sqrt(6-(x^2)/3-(y^2)/2) is Maximum(0,0)