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Rolle's theorem problem

  • #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)
 

Answers and Replies

  • #2
what do i do
 
  • #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?
 
  • #4
well all these are true, so how do u find all numbers c
 
  • #5
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well all these are true, so how do u find all numbers c
[itex]f'(c)=0[/itex]

10 chars....
 
  • #6
HallsofIvy
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Again, what is the conclusion of Rolle's theorem?
 
  • #7
Gib Z
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5
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)
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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