What is the extreme f(x,y)=xy+9/x+3/y ?

The extreme f(x,y)=xy+9/x+3/y is Minimum(3,1)

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extreme f(x,y)=xy+9/x+3/y

extreme points

f (x, y) = x y + \frac{9}{x} + \frac{3}{y}

Minimum (3, 1)

Solution steps

Find the critical points:

(3, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{6}{y ^{3}}

D (x, y) = \frac{108}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(3, 1) :

Minimum

Minimum (3, 1)

What is the extreme f(x,y)=xy+9/x+3/y ?
The extreme f(x,y)=xy+9/x+3/y is Minimum(3,1)