Steiner's calculus problem

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Steiner's problem, asked and answered by Steiner (1850), is the problem of finding the maximum of the function


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


  1. ^ Eric W. Weisstein. "Steiner's Problem". MathWorld. Retrieved December 8, 2010.