(Apologies for the double-quoting; either I never got the original or it somehow got spam-binned by my mail program.)
On Tue, Dec 4, 2018 at 5:37 PM Dan Asimov <dasimov@earthlink.net> wrote: >>>> These are the questions from the recent Putnam Exam that seemed most>> interesting to me. I've changed some typography, and a word or two, for>> clarity. (I haven't tried to solve any yet. If anyone posts a solution,>> maybe include a spoiler warning for that problem number?)...>> A5 Let f : R → R be an infinitely differentiable function satisfying>> f(0) = 0, f(1) = 1, and f(x) ≥ 0 for all x ∈ R. Show that there exist>> a positive integer n and a real number x such that the nth derivative>> of f is negative when evaluated at x:>>>> f^(n)(x) < 0. Surely this can't be right! Why can't we take f(x) = x^2?
-- g