1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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

    also

    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

    daniel_i_l

    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

    gives

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

    which when i do the algebraic manipulation gives

    1+x=(1+c)^2

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

    HallsofIvy

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




Loading...