Find the set of values?

Question

If f(x)=x+1/x, find the set of values for which f increases.

 

Answer: (-∞, -1]U[1, ∞)

 

I know that f'(x)=1-1/x^2=0 and x=1, -1. But what to do next?

Answer 1

You want f'(x) ≥ 0. You get

 

1-1/x² ≥ 0

 

1 ≥ 1/x²

 

x² ≥ 1

 

|x| ≥ 1

 

x ∈ (-∞,-1] ∪ [1,∞)