Derivative increasing without bounds

1. Nov 2, 2011

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

2. Nov 2, 2011

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?

3. Nov 2, 2011

joshmdmd

asymptotes :D