Let $f:R\to R$ a polynomial from degree $n\in N$, such that $f(x) \ge 0$ for all $x \in R$. Explain why n is an even number.
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.