Steiner's calculus problem
Steiner's problem, asked and answered by , 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 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

Functions and mappings
Mathematical optimization