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 points

f (x, y) = \frac{2}{x} + \frac{1}{y} + x y

Solution steps

Find the critical points:

\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

Minimum

f (x, y) = \frac{1}{x} + \frac{1}{y} + x y

f (x) = 7 (x - e^{x})

f (x) = 7 x^{2} - 11 x + 5

f (x) = 26 x^{2} + 80 x + 64

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

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)})