What is the extreme f(x)=((xy)^2+8000x+8000y)/(xy) ?

The extreme f(x)=((xy)^2+8000x+8000y)/(xy) is Minimum(20,20)

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extreme f(x)=((xy)^2+8000x+8000y)/(xy)

extreme points

f (x) = \frac{( x y ) ^{2} + 8000 x + 8000 y}{x y}

Minimum (20, 20)

Solution steps

Find the critical points:

(20, 20)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{16000}{y ^{3}}

D (x, y) = \frac{256000000}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(20, 20) :

Minimum

Minimum (20, 20)

f (x, y) = \frac{1}{( x + y )}

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

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

f (x) = \frac{- x - 8}{10 x ^{2} - 40 x + 27}

f (x, y) = 4 x^{2} + 9 y^{2} - 2 x - 18 x y^{2}

What is the extreme f(x)=((xy)^2+8000x+8000y)/(xy) ?
The extreme f(x)=((xy)^2+8000x+8000y)/(xy) is Minimum(20,20)