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Math Help - Prove the x-coordinate of this equation.

  1. #1
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    Prove the x-coordinate of this equation.

    Not sure if you'd need a picture of the graph or not; don't think you would.

    It just looks like an upside down parabola, but starts at 0 and cuts back through the x-axis.

    The curve (C) has the equation

    y=3x^\frac{1}{2}-x^\frac{3}{2}, x\geq0

    The point A on C is a stationary point (is just a point at where the parabola turns back down [the tiny bit where it's flat]), and C cuts the x-axis at the point B.

    Show that the x-coordinate of B is 3.

    [I would of thought that if i substituted 3 into the above equation, y would equal 0?] it equals -9 however.

    Find the coordinates of A.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    The derivative is 0 at a stationary point--in fact that's the definition
    of stationary point
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