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Math Help - How Do I solve this (using rolle's)?!?! (sin2pi*x) on -1,1 interval(TESTPREP PLZHELP)

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    How Do I solve this (using rolle's)?!?! (sin2pi*x) on -1,1 interval(TESTPREP PLZHELP)

    How Do I solve this

    Sin2πx [-1,1]

    Yes continuous
    Yes differentiable
    f(-1) = f(1)

    So now derive

    2cos2πx = 0

    How do I solve this? The answer in my book says +/- 1/4, +/- 3/4

    How
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    Re: How Do I solve this (using rolle's)?!?! (sin2pi*x) on -1,1 interval(TESTPREP PLZH

    Quote Originally Posted by skinsdomination09 View Post
    How Do I solve this

    Sin2πx [-1,1]

    Yes continuous
    Yes differentiable
    f(-1) = f(1)

    So now derive

    2cos2πx = 0

    How do I solve this? The answer in my book says +/- 1/4, +/- 3/4

    How
    I am going to have to GUESS what the question is....

    I am assuming that you are trying to find the points in c \in [-1,1]  where f'(c)=0

    If so you need to solve the equation

    f'(x)=2\pi \cos(2\pi x)=0 \iff \cos(2\pi x) =0

    Taking the arccosine of both sides gives

    2\pi x =\cos^{-1}(0) \iff 2 \pi x =\frac{\pi}{2} +\pi n, \quad n \in \mathbb{Z}

    x=\frac{1}{4}+\frac{n}{2}, \quad n \in \mathbb{Z}

    This will generate all of the solutions to the problem.
    Thanks from skinsdomination09
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