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: Differentiation problem

  1. Jan 1, 2009 #1
    Let f be continuous on [0,1] and differentiable on (0,1) such that f(0)=f(1), prove that there exist a 0 < c < 1 such that f[tex]\acute{}[/tex](1-c) = -f[tex]\acute{}[/tex](c).

    thanks for any suggestions.
  2. jcsd
  3. Jan 1, 2009 #2
    Just from the givens it made me think of MVT...
  4. Jan 1, 2009 #3
    That was my first impression but it seems to be a little trickier than that.
  5. Jan 1, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    It's a little more complicated, but not much. Define g(x)=f(x)+f(1-x). g(0)=g(1), right?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook