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Math Help - Extrema

  1. #1
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    Extrema

    1) The surface area of a cell in a honey comb is:

    S = 6hs + \frac{3s^2}{2}\left(\frac{\sqrt{3} - \cos(\theta)}{\sin(\theta)}\right)

    where h and s are positive constants and theta is the angle at which the upper faces meet the altitude of the cell. Find the angle theta ( \pi/6 <= \theta <= \pi/2) that minimizes the surface area S.
    Last edited by CaptainBlack; October 25th 2009 at 01:50 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by seuzy13 View Post
    1) The surface area of a cell in a honey comb is:

    S = 6hs + \frac{3s^2}{2}\left(\frac{\sqrt{3} - \cos(\theta)}{\sin(\theta)}\right)

    where h and s are positive constants and theta is the angle at which the upper faces meet the altitude of the cell. Find the angle theta ( \pi/6 <= \theta <= \pi/2) that minimizes the surface area S.
    This has either a calculus like minimum in the interval [\pi/6,\ \pi/2] or the minimum is at an end point of the interval.

    So differentiate and set the derivative to zero and solve for a zero in the given interval, if there is no such root examine the value S at each end of the interval.

    CB
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