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]

Question

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]

anonymous · Answer

Do you know the conditions of Rolle's Theorem?

anonymous · Answer

no i don't !

anonymous · Answer

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

anonymous · Answer

I guess I can join in?

anonymous · Answer

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

anonymous · Answer

just answered this question earlier
on line class?

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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 $x$

anonymous · Answer

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