Question

Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a) = f(b). (Select all that apply.) f(x) = cot x 2 , [π, 8π]

Answer 1

f(a) does not equal f(b) for all possible values of a and b in the interval [π, 3π]
f '(a) does not equal f '(b) for any values in the interval [π, 3π].
There are points on the interval (a, b) where f is not differentiable.
None of these.
There are points on the interval [a, b] where f is not continuous.

Answer 2

Please help me! I am considering among 1,3, and 5

Answer 3

there is a hypothesis for almost every theorem

Answer 4

What do you mean by that?

Answer 5

Nothing is truly true, but instead of guessing why not try learning the theorem itself?

Answer 6

http://mathworld.wolfram.com/RollesTheorem.html

Answer 7

I looked at the theorem but i am not sure if number 1 is neccessary for this answer.

Answer 8

Rolle's theorem is pretty straight forward

Let f be continuous on [a,b] and differentiable on (a,b)
If f(a) = f(b) then there exists a number c in (a,b) such that f'(c)=0.

Hypothesis:
1.f is continuous on [a,b]
2. f is differentiable on (a,b)
3. f(a) = f(b)



conclusion f'(c) = 0 for some number c is (a,b)