Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook