What is the extreme f(x,y)=xy+4/x+2/y ?

The extreme f(x,y)=xy+4/x+2/y is Minimum(2,1)

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extreme f(x,y)=xy+4/x+2/y

extreme points

f (x, y) = x y + \frac{4}{x} + \frac{2}{y}

Minimum (2, 1)

Solution steps

Find the critical points:

(2, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{4}{y ^{3}}

D (x, y) = \frac{32}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(2, 1) :

Minimum

Minimum (2, 1)

f (x) = \frac{2}{x ^{2} + 3}

f (x) = x^{2} (x^{2} - 1)

f (x) = \frac{x}{x ^{2} - 1}, (0, 5)

f (x, y) = x^{2} + 2 y^{2} + x y - 5 x - 6 y

\frac{- x ^{2} + 1}{( x ^{2} + 1 ) ^{2}}

What is the extreme f(x,y)=xy+4/x+2/y ?
The extreme f(x,y)=xy+4/x+2/y is Minimum(2,1)