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Math Help - Application of Maxima and Minima

  1. #1
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    Exclamation Application of Maxima and Minima

    Kindly help me with this problem.

    Two post, one 8 ft high and the other 12 ft. high, stand 15 ft. apart. They are to be stayed by wires attached to a single stake at ground level, the wires running to the top of the posts. Where should the stake be placed to use the least amount of wire ?
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  2. #2
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    Start by drawing a diagram. If you have the first post be the 8ft post and the second be 12ft, then you can call the position of the stake from the 8ft post x.

    You should notice that once you have drawn the diagram with the posts and the wires, you should end up with 2 right angle triangles.

    The first triangle has base x and height 8, so the wire will be \sqrt{8^2 + x^2}.

    The second triangle has base 15 - x and height 12, so the wire will be \sqrt{12^2 + (15 - x)^2}.


    So you are minimising L = \sqrt{8^2 + x^2} + \sqrt{12^2 + (15 - x)^2}.

    You will need to simplify this, then take the derivative to find the critical points.
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  3. #3
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    Hello, jasonlewiz!

    Two post, one 8 ft high and the other 12 ft. high, stand 15 ft. apart.
    They are to be stayed by wires attached to a single stake at ground level,
    the wires running to the top of the posts.
    Where should the stake be placed to use the least amount of wire ?

    Here is a diagram for Prove It's excellent solution.


    Code:
                                o C
                               *|
                              * |
                             *  |
        A o                 *   |
          | *              *    | 12
          |   *           *     |
        8 |     *        *      |
          |       *     *       |
          |         *  *        |
        B o - - - - - o - - - - o D
          :     x     P   15-x  :
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