Derivative increasing without bounds

[apiwowar]

if f'(x) > 0 for all real values of x then x increases without bounds. I thought that was true but in the back of the book it says false and uses f(x)=2x/sqrt(x²+2) as an example. i worked out the derivative and got f'(x) = 4/(x²+2)^3/2.

how does that show that the first sentence is false? I'm quite confused abou this

 

[Dick]

You got the derivative right. And it's always positive, yes. But f(x) doesn't increase without bound. It approaches 2 as x->inf. Can you show that?

 

[joshmdmd]

asymptotes :D