Steiner's calculus problem

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

[1]

It is named after Jakob Steiner.

The maximum is at , where e denotes the base of the natural logarithm. One can determine that by solving the equivalent problem of maximizing

Applying the first derivative test, the derivative of is

so is positive for and negative for , which implies that – and therefore – is increasing for and decreasing for Thus, is the unique global maximum of

References

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