What is the extreme f(x,y)=(13720)/x+(13720)/y+5xy ?

The extreme f(x,y)=(13720)/x+(13720)/y+5xy is Minimum(14,14)

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extreme f(x,y)=(13720)/x+(13720)/y+5xy

extreme points

f (x, y) = \frac{13720}{x} + \frac{13720}{y} + 5 x y

Minimum (14, 14)

Solution steps

Find the critical points:

(14, 14)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{27440}{y ^{3}}

D (x, y) = \frac{752953600}{x ^{3} y ^{3}} - 25

Check the sign of at each critical point

Check critical point

(14, 14) :

Minimum

Minimum (14, 14)

f (x) = 4 x^{3} - 8 x

f (x) = 12 x^{5} + 45 x^{4} - 360 x^{3} + 6

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

f (x) = x^{3} - 4 x^{2} - x + 1

f (x, y) = \frac{20000}{3 + x ^{2} + y ^{2}}

What is the extreme f(x,y)=(13720)/x+(13720)/y+5xy ?
The extreme f(x,y)=(13720)/x+(13720)/y+5xy is Minimum(14,14)