# Thread: Application of Maxima and Minima

1. ## 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 ?

2. 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.

3. 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  :