Optimization for products of concave functions

Ifh denotes the product of finitely many concave non-negative functions on a compact interval a, b], then it is shown that there exist pointsα andβ witha≤α≤β≤b such thath is strictly increasing on α, α), constant on (α, β), and strictly decreasing on (β, b]. This structure theorem leads to an extension of several classical optimization results for concave functions on convex sets to the case of products of concave functions.