What is the extreme f(x,y)=(20480)/x+(20480)/y+5xy ?

The extreme f(x,y)=(20480)/x+(20480)/y+5xy is Minimum(16,16)

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extreme f(x,y)=(20480)/x+(20480)/y+5xy

extreme points

f (x, y) = \frac{20480}{x} + \frac{20480}{y} + 5 x y

Minimum (16, 16)

Solution steps

Find the critical points:

(16, 16)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{40960}{y ^{3}}

D (x, y) = \frac{1677721600}{x ^{3} y ^{3}} - 25

Check the sign of at each critical point

Check critical point

(16, 16) :

Minimum

Minimum (16, 16)

f (x) = 2 x^{3} + 6 x^{2} - 144 x + 2, - 6 \leq x \leq 5

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

f (x) = (9 sin (x) - 9) (2 cos (x) 3)

f (x) = - x^{3} - 4.5 x^{2} + 12 x - 2

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

What is the extreme f(x,y)=(20480)/x+(20480)/y+5xy ?
The extreme f(x,y)=(20480)/x+(20480)/y+5xy is Minimum(16,16)