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Math Help - Need help creating an expression/function for a specific curve

  1. #1
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    Need help creating an expression/function for a specific curve

    Hello everyone. I'm not sure if this question falls more into the algebra side of things or the trig side of things, but I figured this would be a good place to start.

    Here's the problem. I need to find a function for a curve where f(x) = 0 when x = 0 or x = 1.

    Now, the obvious solution is f(x) = sin(x * pi)

    Here is the problem, a sin curve is too gradual. I need the curve to be close to its peak from....lets say x = .2 to x = .8, arbitrarily speaking.

    I've tried taking a basic parabola, reflecting it across the x axis, and trying to adjust it's parameters to make a functional curve, but it hasn't gone so well.

    Can any one educate me on creating this function, or maybe if its easier can I simply change the slope of the sin curve? (I don't think I can, but it's worth asking)
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  2. #2
    MHF Contributor
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    Hi

    If I have well understood you can select f(x) = x^a(1-x)^b where a and b are parameters

    The lower values you chose for a and b, the "flatter" the curve is
    You can take for instance a=b=0.1
    Last edited by running-gag; July 4th 2009 at 01:01 PM. Reason: Precision added
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  3. #3
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    Quote Originally Posted by running-gag View Post
    Hi

    If I have well understood you can select f(x) = x^a(1-x)^b where a and b are parameters

    The lower values you chose for a and b, the "flatter" the curve is
    You can take for instance a=b=0.1
    Thank you, that is exactly what I needed. Perhaps I would've noticed if I had remembered to factor x^2 into x * x, but it's been a while.
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