Results 1 to 3 of 3

Math Help - Derivatives - Proof

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    70

    Derivatives - Proof

    How can i prove that;

    if f is a differentiable function on [a,b] where f '(a) < 0 and f '(b)>0, there exists a point c in the set of (a,b) at which f '(c) = 0, and i can't assume the function is continuous.

    This makes perfect sense to me intuitively yet i'm having trouble proving it am not sure which theorem helps here if any and where exactly to start.

    Cheers,
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by monster View Post
    How can i prove that;

    if f is a differentiable function on [a,b] where f '(a) < 0 and f '(b)>0, there exists a point c in the set of (a,b) at which f '(c) = 0, and i can't assume the function is continuous.

    This makes perfect sense to me intuitively yet i'm having trouble proving it am not sure which theorem helps here if any and where exactly to start.

    Cheers,
    Do you know the intermediate value theorem for derivatives?

    http://en.wikipedia.org/wiki/Darboux...orem_(analysis)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2008
    Posts
    70
    Ah cheers very helpfull!

    This wasn't tought in lectures but even as i was working on the problem i was wondering if IVT would hold for derivatives.

    Cheers
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proof: working with derivatives, possibly mean value theorem?
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: May 4th 2010, 05:03 AM
  2. Proof Involving Partial Derivatives Chain Rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 26th 2010, 12:03 AM
  3. Third Law of Logs Proof (using derivatives)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 1st 2009, 06:15 PM
  4. Linalg - Proof involving distinct roots and derivatives
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 3rd 2009, 08:16 PM
  5. Replies: 1
    Last Post: October 13th 2007, 01:19 AM

Search Tags


/mathhelpforum @mathhelpforum