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    A curve c has equation y=f(x), y>0. At any point P on the curve, the gradient of C is proportional to the product of the x and y coordinates of P. The point A with coordinates (4,2) Is on C and the gradient of C at A is 1/2.

    Show that dy/dx = xy/16

    Im realy unsure on the wording of the question and how to auctaly answer it >.< Any help please?

    the gradient is proportional to the product of the x and y coordinates

    i.e. dy/dx = kxy

    plug in the values you have

    1/2 = 8k
    k = 1/16

    now you have k, substitute it back into dy/dx = kxy

    dy/dx = xy/16
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Updated: February 8, 2010

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