Steiner's calculus problem
From Infogalactic: the planetary knowledge core
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
References
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