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    Derivatives, Tangent Lines and Rates of Change

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    1. A curve has the equation x²-4xy+y²=24
    a) Show that
    dy/dx= (x-2y)/(2x-y)

    b) find the equation for the tangent to the curve at the point P (2, 10)
    The tangent to the curve at Q is parrallel to the tangent at P
    c) find the coordinates of Q

    2. The diagram shows the coss-section of a vase. The volume of the water
    in the vase, V cm³, when the depth of water in the vase is h cm is given by
    V=40 pi (e^0.1 h^-1)
    The vase is initially empty and water is poured into it at a constant rate
    of 80 cm³s-¹
    Find the rate at which the depth of water in the vase is increasing
    a) when h=4

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    https://brainmass.com/math/derivatives/derivatives-tangent-lines-and-rates-of-change-115969

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    Derivatives, Tangent Lines and Rates of Change are investigated. The solution is detailed and well presented.

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