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

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

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

extreme points

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)

\frac{x}{x ^{3} + x ^{2} + 9}

f (x) = x^{4} - 128 x^{2} + 5

x y - 3 x^{2} - 2 y^{2}

\frac{2 x}{x ^{2} + x - 20} \frac{3 x}{x ^{2} + 4 x - 5}

f (x) = 2 x^{3} - 12 x^{2} + 14

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