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Math Help - Curve, gradient and point.

  1. #1
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    Curve, gradient and point.

    a - ( (b) / (c+x^2) )

    The line goes through (2, 2/3) and the gradient of the curve is at its maximum at x= root6/3 (square root of 6 divided by 3)

    Prove a = 1, b = 2, c = 2.

    Can I please have a detailed solution to this? I've tried so many ways, been hours already. It was in the dydx and integration section.
    Last edited by mr fantastic; August 17th 2011 at 01:54 PM. Reason: Re-titled.
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  2. #2
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    Re: Help!

    sorry c wasnt 3, c = 2
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  3. #3
    MHF Contributor Siron's Avatar
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    Re: Help!

    For example, if the curve goes throught the point \left(2,\frac{2}{3}\right) that means:
    \frac{2}{3}=a-\frac{b}{c+4}

    Have you tried something this way? Also with the other given information? ...
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  4. #4
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    Re: Help!

    Yes I was aware it was a curve. I've tried something like that. Still ended up with 2 unknowns. and 3 in the other.

    And the point where the gradient is its max. Stuck on how to get that equation. Or use that info. Would it be double derivative?
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Help!

    Yes, calculate the second derivative of the function, then let f''(x)=0 and enter x=\frac{\sqrt{6}}{3} therefore you can calculate c.
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