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

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

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

extreme points

f (x, y) = 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) = x y - 7 x y + 200 x

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

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

f (x, y) = - 5 x^{2} + 4 x y - y^{2} + 16 x + 10

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

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