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Homework Help: Rolle's theorem problem

  1. Mar 30, 2007 #1
    verify that the 3 hypothesis of rolle's theorem on the given interval . then find all the numbers c that satisfy the conclusion of rolle's theorem.

    f(x)=sin2piex [-1,1]

    i found the derivative cos 2pie x, but what do i do, and what does the theorem mean when f is differentiable on the open interval (a,b)
     
  2. jcsd
  3. Mar 30, 2007 #2
    what do i do
     
  4. Mar 31, 2007 #3

    HallsofIvy

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    First you go back and read the statement of Rolle's theorem? You are asked to "verify that the 3 hypothesis of rolle's theorem [are true] on the given interval". What are the 3 hypotheses? Being differentiable on the interior of the interval is one of them.

    You are also asked to "find all the numbers c that satisfy the conclusion of rolle's theorem." Okay, what is the conclusion of Rolle's theorem?
     
  5. Mar 31, 2007 #4
    well all these are true, so how do u find all numbers c
     
  6. Mar 31, 2007 #5
    [itex]f'(c)=0[/itex]

    10 chars....
     
  7. Apr 1, 2007 #6

    HallsofIvy

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    Again, what is the conclusion of Rolle's theorem?
     
  8. Apr 1, 2007 #7

    Gib Z

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    No The derivative of [itex] \sin (2\pi x ) [/itex] is not that. Using the chain rule it is [itex]2\pi \cos (2\pi x)[/itex]
     
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