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!

Prove that f(100) < 100

  1. Aug 26, 2011 #1
    1. The problem statement, all variables and given/known data


    For f(0) = 0, and that f'(x) = [tex]\frac{1}{1 + e^{-f(x)}}[/tex], prove that f(100) < 100


    3. The attempt at a solution

    I did

    [tex]\f(100) = \int_{0}^{100} \frac{dx}{1 + e^{-f(x)}}[/tex]

    Unfortunately, I got f(100) back...
     
  2. jcsd
  3. Aug 26, 2011 #2

    fzero

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  4. Aug 26, 2011 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    That's already ok. Can you prove now that the integral must be <100??

    First, can you prove that

    [tex]\frac{1}{1+e^{-f(x)}}\leq 1[/tex]
     
  5. Aug 26, 2011 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    For y > = 0 we have 1/(1+exp(-y)) = exp(y)/[1+exp(y)] <= 1.

    RGV
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Prove that f(100) < 100
  1. N^3 + 100 (Replies: 3)

Loading...