What is the extreme f(x,y)=xy+(27)/x+(27)/y ?

The extreme f(x,y)=xy+(27)/x+(27)/y is Minimum(3,3)

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extreme f(x,y)=xy+(27)/x+(27)/y

extreme points

f (x, y) = x y + \frac{27}{x} + \frac{27}{y}

Minimum (3, 3)

Solution steps

Find the critical points:

(3, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{54}{y ^{3}}

D (x, y) = \frac{2916}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(3, 3) :

Minimum

Minimum (3, 3)

2 x^{3} + 3 x^{2} - 12 x + 1

f (x) = 8 x - x^{4}

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

f (x) = - x^{2} - 6 x + 9

f (x) = - x^{2} - 6 x - 8

What is the extreme f(x,y)=xy+(27)/x+(27)/y ?
The extreme f(x,y)=xy+(27)/x+(27)/y is Minimum(3,3)