What is the extreme f(x)=xy+8/x+8/y ?

The extreme f(x)=xy+8/x+8/y is Minimum(2,2)

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extreme f(x)=xy+8/x+8/y

extreme points

f (x) = x y + \frac{8}{x} + \frac{8}{y}

Minimum (2, 2)

Solution steps

Find the critical points:

(2, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{16}{y ^{3}}

D (x, y) = \frac{256}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(2, 2) :

Minimum

Minimum (2, 2)

f (x, y) = ln (x y - 1)

f (x) = 3 x^{3} - 6 x^{2} + 1

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

f (x) = \frac{1}{x ^{2} + 2 x + 9}

f (x) = (x - 3)^{4}

What is the extreme f(x)=xy+8/x+8/y ?
The extreme f(x)=xy+8/x+8/y is Minimum(2,2)