What is the extreme f(x,y)=xy+(64)/x+(64)/y ?

The extreme f(x,y)=xy+(64)/x+(64)/y is Minimum(4,4)

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extreme f(x,y)=xy+(64)/x+(64)/y

extreme points

f (x, y) = x y + \frac{64}{x} + \frac{64}{y}

Minimum (4, 4)

Solution steps

Find the critical points:

(4, 4)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{128}{y ^{3}}

D (x, y) = \frac{16384}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(4, 4) :

Minimum

Minimum (4, 4)

What is the extreme f(x,y)=xy+(64)/x+(64)/y ?
The extreme f(x,y)=xy+(64)/x+(64)/y is Minimum(4,4)