What is the extreme f(x)=xy+(50)/x+(20)/y ?

The extreme f(x)=xy+(50)/x+(20)/y is Minimum(5,2)

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extreme f(x)=xy+(50)/x+(20)/y

extreme points

f (x) = x y + \frac{50}{x} + \frac{20}{y}

Minimum (5, 2)

Solution steps

Find the critical points:

(5, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{40}{y ^{3}}

D (x, y) = \frac{4000}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(5, 2) :

Minimum

Minimum (5, 2)

f (x, y) = (5 - x) (5 - y) (x + y - 5)

\frac{- 3 x + 66}{( x - 86 ) ^{5}}

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

x^{\frac{2}{3}}

f (x) = 3 - x - \frac{25}{x}, x > 0

What is the extreme f(x)=xy+(50)/x+(20)/y ?
The extreme f(x)=xy+(50)/x+(20)/y is Minimum(5,2)