What is the extreme f(x,y)= 2/x+1/y+xy ?

The extreme f(x,y)= 2/x+1/y+xy is Minimum(\sqrt[3]{4}, 1/(2^{1/3)})

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extreme f(x,y)= 2/x+1/y+xy

extreme

Minimum (34, \frac{1}{2 ^{\frac{1}{3}}})

Solution steps

Find the critical points:

(34, \frac{1}{2 ^{\frac{1}{3}}})

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{2}{y ^{3}}

D (x, y) = \frac{8}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(34, \frac{1}{2 ^{\frac{1}{3}}}) :

Minimum

Minimum (34, \frac{1}{2 ^{\frac{1}{3}}})

What is the extreme f(x,y)= 2/x+1/y+xy ?
The extreme f(x,y)= 2/x+1/y+xy is Minimum(\sqrt[3]{4}, 1/(2^{1/3)})