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!

Mean Value Theorom

  1. May 26, 2008 #1
    Let f(x)=1/(1+x)

    Use the Mean Value Theorom (for the derivative of a function) to prove that f(x)>=1-x for x>=0


    Mean Value Theorom states:

    [f(b)-f(a)]/ [b-a]= f'(c) where c is an element of [a,b]
  2. jcsd
  3. May 26, 2008 #2


    User Avatar
    Gold Member

    what do you get for f(x) when you use the MVT with b=x, a=0? What are the limits on c?
  4. May 26, 2008 #3
    [f(b) - f(a)]/[b-a]=f'(c) for b=x and a=0


    [1/(1+x) - 1]/x=-1/(1+c)^2

    which when i do the algebraic manipulation gives


    i don't know how to make a relation between 1-x and 1/(1+x)
  5. May 26, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    What is the largest possible value for 1/(1+c)2?
  6. May 26, 2008 #5
    You already went too far, you want to keep f (don't substitute) on the lhs to get that inequality, so keep it like this:
    [tex](f(x) -1)/x = -1/(1+c^2)[/tex]
    and then follow HallsofIvy's hint.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Mean Value Theorom
  1. Mean Value Theorem (Replies: 3)

  2. Mean Value Theorem (Replies: 2)