Results 1 to 2 of 2

Math Help - intermediate value theorem question

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    1

    intermediate value theorem question

    A recent calc problem assigned to me was:
    Suppose that f is a continuous function on [0,1]. If 0 < f(x) < 1 for all x E[0,1] show that there is a point c such that f(c) = c.

    I figured I'd be using the intermediate value theorem at least, but I can't figure out how to prove that a point c would produce a function value of c. It seems to me that that wouldn't be the case. Anyways, any help would be much appreciated. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2009
    Posts
    130
    Counter-example: f(x) = x + 1

    The theorem is true if f is bounded and continuous on R. To prove it, consider the function g(x) = f(x) - x. Use the fact that f is bounded and try to show that g has at least one root.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. intermediate value theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2010, 08:30 PM
  2. Intermediate Value Theorem question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 22nd 2009, 08:54 AM
  3. Question about Intermediate Value Theorem on diff. Topologies
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 8th 2009, 04:37 PM
  4. intermediate value theorem question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 22nd 2008, 12:49 AM
  5. intermediate value theorem/rolle's theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 8th 2007, 02:55 PM

Search Tags


/mathhelpforum @mathhelpforum