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Derivative increasing without bounds

  1. Nov 2, 2011 #1
    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. jcsd
  3. Nov 2, 2011 #2


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    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?
  4. Nov 2, 2011 #3
    asymptotes :D
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