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Math Help - Rolles Theorem

  1. #1
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    Rolles Theorem

    Determine whether Rolles Theorem can be applied to f(x)=cos(pi*x) on the closed interval [ -1/6, 1/6]. If so, find all #'s c in the open interval (-1/6,1/6) such that f'(c) =0.

    My results: I started by checking if it is continuous, which it is. Then if its differentiable, which it is. The end points ( -1/6, 1/6) also return the same value. So then I send the derivative to zero

    which looked like 0= -pi*sin(pi*x)

    which equals 2pi.. therefore Rolles Theorem doesnt not apply. Correct me if I'm wrong?
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  2. #2
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    What about c=0?
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  3. #3
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    you mean f'(c)=0?

    b/c c=0 = 1 which is outside the intervals as well... right?
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  4. #4
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    Quote Originally Posted by action812 View Post
    you mean f'(c)=0?
    b/c c=0 = 1 which is outside the intervals as well... right?
    That is nonsense. \frac{-1}{6}<0<\frac{1}{6} .
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  5. #5
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    so the derivative set to zero = zero.

    therefore the asnwer is x= 0 for the whole problem? correct?
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