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)

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

f (x, y) = 5 (x - 3)^{2} - 6 y^{2} + 4 x y

f (x) = x^{3} - 6 x^{2} + 4 x - 2

f (x, y) = ln (x) + ln (y) - ln (x + y) - \frac{x}{12} - \frac{y}{3}

f (x, y) = 8 x^{4} + y^{2} - 16 x y

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)