September 2015 Problem of the Month

Let f(x),g(x) be continuous functions with continuous first derivatives for all real x such that fg’-gf’ is never zero. Prove that between any two consecutive roots of f(x)=0 there is exactly one root of g(x)=0.

Reward for best solution: A copy of the book “Godel’s proof” By Ernest Nagel and James R. Newman.Donated by Dr. Milé [...]