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Math Help - finding a function

  1. #1
    Junior Member
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    finding a function

    So here's my problem:

    Given f\prime\prime(x)=-9sin(3x)
    f\prime(0)=-4
    and f(0)=-1

    Find f(\frac{\pi}{2})=

    Any suggestions are greatly appreciated.
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  2. #2
    Member mathemagister's Avatar
    Joined
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    Quote Originally Posted by ascendancy523 View Post
    So here's my problem:

    Given f\prime\prime(x)=-9sin(3x)
    f\prime(0)=-4
    and f(0)=-1

    Find f(\frac{\pi}{2})=

    Any suggestions are greatly appreciated.
    f'(x) = \int f''(x)\ dx = \int -9\sin{(3x)}\ dx = 3\cos{(3x)} + C

    f'(0) = -4 \implies 3\cos{(3\cdot 0)} + C = -4 \implies 3 + C = -4 \implies C = -7

    Now you know f'(x) = 3\cos{(3x)} - 7

    f(x) = \int f\ '(x)\ dx = \int 3\cos{(3x)} - 7 \ dx = \sin{(3x)}-7x +D

    f(0)=-1 \implies \sin{(3\cdot 0)}-7\cdot 0 +D = -1 \implies D = -1

    f(x) = \sin{(3x)}-7x -1

    f\left(\frac{\pi}{2}\right) = \sin{\left(\frac{3\pi}{2}\right)}- \frac{7\pi}{2}-1=-1-\frac{7\pi}{2}-1 = \boxed{-\frac{7\pi}{2}-2}

    Hope that helps

    Mathemagister
    Last edited by mathemagister; April 3rd 2010 at 12:26 PM. Reason: A person I referred to deleted his post.
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