## anonymous 3 years ago Determine whether Rolle's Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. If Rolle's Theorem does not apply, enter DNE) f(x) = ln(5 − sin(x)) on [0, 2π]

1. anonymous

Do you know the conditions of Rolle's Theorem?

2. anonymous

no i don't !

3. anonymous

The function has to be continuous and differentiable and f(a)=f(b)

4. anonymous

I guess I can join in?

5. anonymous

yeah i do but i tried and didn't get the right answer

6. anonymous

just answered this question earlier on line class?

7. anonymous

Okay so you know rolle's theorem states that if you have a continuous and differentiable function on [a,b] and (a,b) then there exists a number c where f'(c) is equal to zero on that interval.

8. anonymous

So you would differentiate and set y= 0, then solve for x.

9. anonymous

sinc $$sin(0)=\sin(2\pi)=0$$ you get $$f(0)=f(2\pi)=\ln(5)$$ take the derivative, set it equal to zero and solve for $$x$$

10. anonymous

okay ! thanks for the help and yes online class :(