Write the minimum value of f(x) = x + 1/x , x > 0. ​

Question

Write the minimum value of  f(x) = x + \(\frac{1}{x}\), x > 0.

Answer 1

Since, 

x > 0. 

By AM ≥ GM property;

 (x + \(\frac{1}{x}\)) ≥ \(\sqrt x\) \(\times\)\(\frac{1}{\sqrt x}\)

So, 

Minimum value of (x + \(\frac{1}{x}\)) is 1 which occurs when x = \(\frac{1}{x}\) 

i.e, 

x = 1.