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

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

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

extreme points

f (x, y) = \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) = 4 x^{2} - 8 x + 7 y^{2} + 8

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

f (x) = 2 (csc (x) + sec (x))

f (x, y) = x e^{y} - ln (x)

y = \frac{5}{x}

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