What is the extreme f(x)=(69120)/x+(69120)/y+5xy ?

The extreme f(x)=(69120)/x+(69120)/y+5xy is Minimum(24,24)

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extreme f(x)=(69120)/x+(69120)/y+5xy

extreme points

f (x) = \frac{69120}{x} + \frac{69120}{y} + 5 x y

Minimum (24, 24)

Solution steps

Find the critical points:

(24, 24)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{138240}{y ^{3}}

D (x, y) = \frac{19110297600}{x ^{3} y ^{3}} - 25

Check the sign of at each critical point

Check critical point

(24, 24) :

Minimum

Minimum (24, 24)

f (x) = x^{\frac{2}{3}} (x + 1)

f (x) = x^{2} + 4 x (\frac{4000}{x ^{2}})

f (x) = (1)^{\frac{1}{3}} \cdot (- 9)

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

f (x) = x^{\frac{2}{3}} (x + 4)

What is the extreme f(x)=(69120)/x+(69120)/y+5xy ?
The extreme f(x)=(69120)/x+(69120)/y+5xy is Minimum(24,24)