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