1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof using mean-value theorem

  1. Nov 29, 2007 #1
    use the mean-value theorem to show that if f is continous at x and at x+h and is differentiable between these 2 numbers, then f(x+h) - f(x) = f'(x+ah)h for some number a between 0 and 1.

    mvt: if f is diff'ble on (a,b) and continuous on [a,b] then there is at least one number c in (a,b) for which f'(c)=[f(b)-f(a)]/(b-a)

    any help will be appreciateddd..i don't know where to start :(
  2. jcsd
  3. Nov 29, 2007 #2
    Try thinking of the expression

    f(x+h) = f(x) = hf'(x+ah) where 0 < a < 1

    as another form of expressing the mean value theorem . You know that f is continuous on [x, x+h] and differentiable on (x, x+h). So now apply the MVT. I don't want to give much more info yet because I'd be giving up the whole proof. Give it a try and see how far you can get with it.
    Last edited: Nov 29, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Proof using mean-value theorem