Results 1 to 2 of 2

Math Help - Use EVT and Fermats to prove there is a c such that f'(c)=0

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    5

    Use EVT and Fermats to prove there is a c such that f'(c)=0

    If f is differentiable on the interval [a,b] and f'(a)<0<f'(b), prove that there is a c with a<c<b for which f'(c)=0. (Hint: Use the Extreme Value Theorem and Fermat's Theorem.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: Use EVT and Fermats to prove there is a c such that f'(c)=0

    Quote Originally Posted by NWeid1 View Post
    If f is differentiable on the interval [a,b] and f'(a)<0<f'(b), prove that there is a c with a<c<b for which f'(c)=0. (Hint: Use the Extreme Value Theorem and Fermat's Theorem.)
    Are you locked into using the EVT and Fermat's Theorem? A more intuitive approach would be to try to use the Intermediate Value Theorem on f'(x). The only catch there is that I'm not sure you know that f' is continuous.

    If you must use Fermat's Theorem, then you need to show that there is a local extremum of f in (a,b). If you could show that, then you could invoke Fermat's Theorem, and you'd be done. How could you show that there is a local extremum in (a,b)?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fermats last theorem solution, try 2.
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 14th 2010, 07:06 AM
  2. Fermats Little Theorem
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: September 25th 2010, 04:18 PM
  3. Prove n is prime (linked to Fermats little theorem)
    Posted in the Number Theory Forum
    Replies: 11
    Last Post: April 17th 2010, 05:19 PM
  4. Fermats Last Theorem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: November 18th 2008, 07:23 AM
  5. Fermats criteria - Correct?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 15th 2008, 08:06 AM

Search Tags


/mathhelpforum @mathhelpforum