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Math Help - Trigonometry, Stationary Points and the Second Derivative

  1. #1
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    Trigonometry, Stationary Points and the Second Derivative

    I'm having trouble getting the answer to this particular question out;

    Given that the \frac{d^2y}{dx^2} is equal to 9\sin3x;
    1. Find y if there is a stationary point at (\frac{\pi}{2}, 1)
    2. Show that \frac{d^2y}{dx^2} + 9y = 0
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    What you have here

    Quote Originally Posted by Flay View Post
    I'm having trouble getting the answer to this particular question out;

    Given that the \frac{d^2y}{dx^2} is equal to 9\sin3x;
    1. Find y if there is a stationary point at (\frac{\pi}{2}, 1)
    2. Show that \frac{d^2y}{dx^2} + 9y = 0

    is a differntial equation...here is what you do...since \frac{d^2y}{dx^2}=9sin(3x)......ok now seperate to get d^2y=9sin(3x)dx then integrate to get y'=-3cos(3x)+C...now stop before we get to y we must find that c...we know there is a stationary point at c which means the slope is 0 at \frac{\pi}{2{ which means that y'=0...so thefore 0=-3cos\bigg(3\cdot\frac{\pi}{2}\bigg)+C solve and you see c=0...next integrate again to get y and you see that y=-sin(3x)+C now using that condition again we know that 1=-sin\bigg(3\cdot\frac{\pi}{2}\bigg)+C_1 solving we get x=0..therfore y=-sin(3x)


    for part two just add nine times what we just found to what \frac{d^2y}{dx^2} is to verify its zero
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  3. #3
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    Got it. I was making yet another stupid mistake.
    Last edited by Flay; April 7th 2008 at 10:57 PM.
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