What Does Rolle's Theorem Mean for Differentiable Functions on Closed Intervals?

[afcwestwarrior]

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)

 

[afcwestwarrior]

what do i do

 

[HallsofIvy]

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?

 

[afcwestwarrior]

well all these are true, so how do u find all numbers c

 

[f(x)]

well all these are true, so how do u find all numbers c

$f'(c)=0$

10 chars...

 

[HallsofIvy]

Again, what is the conclusion of Rolle's theorem?

 

[Gib Z]

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 $\sin (2\pi x )$ is not that. Using the chain rule it is $2\pi \cos (2\pi x)$