Hello, cazimi!

This is one of the more unpleasant problems . . .

Two posts, one 3m high and the other 6m high, stand 10m apart.

They are to be stayed by wires attached to a single stake at ground level,

the wires running to the tops of the posts.

Where should the stake be placed to use the least amount of wire? Code:

*C
* |
* |
* |
A* * | 6
| * * |
3 | * * |
| * * |
B* - - - - - * - - - - - - - *D
: x P 10-x :

AB is the 3-meter pole; CD is the 6-meter pole.

They are 10 meters apart: BD = 10.

The wire runs from A to a point P on the ground, then up to C.

Let x = BP, then PD = 10 - x.

From the right triangles (and Pythagorus), we have:

. . . . . . . . ______ . . . . . . . .___________

. . AP .= .√x² + 3², . CP .= .√(10 - x)² + 6²

The length of the wire is: .L .= .[x² + 9]^½ + [(10 - x)² + 36]^½

And *that* is the function you must minimize.

I'll wait in the car . . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

There is a very clever geometric approach to this problem

. . which eliminates the need for all that Calculus.

I'll let someone else explain it.