Steiner's calculus problem
It is named after Jakob Steiner.
The maximum is at , where e denotes the base of natural logarithms. One can determine that by solving the equivalent problem of maximizing
The derivative of can be calculated to be
It follows that is positive for and negative for , which implies that (and therefore ) increases for and decreases for Thus, is the unique global maximum of
- Eric W. Weisstein. "Steiner's Problem". MathWorld. Retrieved December 8, 2010.
- Steiner, J. (1850), "Über das größte Product der Theile oder Summanden jeder Zahl", Crelle, 40: 208