anonymous
  • anonymous
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]
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Do you know the conditions of Rolle's Theorem?
anonymous
  • anonymous
no i don't !
anonymous
  • anonymous
The function has to be continuous and differentiable and f(a)=f(b)

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anonymous
  • anonymous
I guess I can join in?
anonymous
  • anonymous
yeah i do but i tried and didn't get the right answer
anonymous
  • anonymous
just answered this question earlier on line class?
anonymous
  • 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.
anonymous
  • anonymous
So you would differentiate and set y= 0, then solve for x.
anonymous
  • 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 \(x\)
anonymous
  • anonymous
okay ! thanks for the help and yes online class :(

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