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

    Dick

    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