Thread: 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 ?

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 .

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 and height , so the wire will be .

The second triangle has base and height , so the wire will be .


So you are minimising .

You will need to simplify this, then take the derivative to find the critical points.

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  :