I have $n$ polynomials, each one is positive over a certain range and the maximum value each can attain is 1. Also each polynomial has atmost one peak(maximum). Is there some way that I can show that the sum of these polynomials also has one peak atmost. Each polynomial is something like $x^3(1-x)^2$ where $0\leq x\leq 1$.
is this information enough.