1. The problem statement, all variables and given/known data Let f be a polynomial function of degree n such that f(x) ≥ 0 for all x (note that n must be even). Prove that f + f' +f'' + f''' + ... + f^(n) ≥ 0. 2. Relevant equations I believe that is all - the derivative of some term in the polynomial ax^n is anx^(n-1). 3. The attempt at a solution I attempted induction on n (stepping up by two, not one, each time), actually writing out the final summed polynomial in terms of its coefficients, etc. but have made no real progress. Thank you for hints/solutions in advance! (if you have a suggestive hint, I actually would appreciate that MORE than a solution, but if you want to give a solution I'd still be happy).