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Math Help - Optimizing

  1. #1
    Junior Member
    Joined
    Sep 2009
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    65

    Optimizing

    A light is suspended at a height h above the floor (see figure below). The illumination at the point P is inversely proportional to the square of the distance from the point P to the light and directly proportional to the cosine of the angle θ. Let d = 2 ft.

    (a) Express the illumination in terms of h only. Use k for the proportionality constant.

    (b) How far from the floor should the light be to maximize the illumination at the point P? (in ft)


    I am not sure how to approach this problem, I think I am missing something. Attached is a photo of what the problem looks like.
    Attached Thumbnails Attached Thumbnails Optimizing-yeah.gif  
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