What is the extreme f(x,y)=6x^{1/6}y^{1/6}-x-y ?

The extreme f(x,y)=6x^{1/6}y^{1/6}-x-y is Maximum(1,1)

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extreme f(x,y)=6x^{1/6}y^{1/6}-x-y

extreme points

f (x, y) = 6 x^{\frac{1}{6}} y^{\frac{1}{6}} - x - y

Maximum (1, 1)

Solution steps

Find the critical points:

(1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{5 x ^{\frac{1}{6}}}{6 y ^{\frac{11}{6}}}

D (x, y) = \frac{2}{3 x ^{\frac{5}{3}} y ^{\frac{5}{3}}}

Check the sign of at each critical point

Check critical point

(1, 1) :

Maximum

Maximum (1, 1)

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

f (x) = 2 x - ln (x)

f (x) = - x^{2} - 16 x - 62

1 + e^{- x}

f (x) = 32 sin (\frac{π}{3} x) + 42

What is the extreme f(x,y)=6x^{1/6}y^{1/6}-x-y ?
The extreme f(x,y)=6x^{1/6}y^{1/6}-x-y is Maximum(1,1)