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Math Help - Graphing Using Calculus

  1. #1
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    Graphing Using Calculus

    y^2 = (a^2 x) / (2a - x )

    Find points of inflexion and sketch the curve.

    By implicitly differentiating Ive got a value for dy/dx

    = 2a^3 / (2a-x)^2 ( 2y)

    However, I do not know how to do from here. Do I implicitly differentiate again or ... and how do i do that?
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  2. #2
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    Quote Originally Posted by Lukybear View Post
    y^2 = (a^2 x) / (2a - x )

    Find points of inflexion and sketch the curve.

    By implicitly differentiating Ive got a value for dy/dx

    = 2a^3 / (2a-x)^2 ( 2y)

    However, I do not know how to do from here. Do I implicitly differentiate again or ... and how do i do that?
    First of all, the graph is defined for 0<= x<=2a

    y=\sqrt{\frac{a^2x}{2a-x}} , 0<= x<=2a


    \frac{dy}{dx}=\sqrt{\frac{a^4}{(2a-x)^3x}}


    \frac{d^2y}{dx^2}=\frac{1}{2}\sqrt{\frac{1}{(2a-x)^5x^3}}\cdot (-4x+2a)

    Set that equals 0, x=1/2 a

    Hence the point of inflection is (1/2 a , a sqrt(1/3))
    Last edited by mathaddict; August 28th 2010 at 08:57 AM.
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