Rational function/R/Derivative/Polynomial if and only if derivative is zero/Exercise

Let ${}D\subseteq \mathbb {R}$ and

$F\colon D\longrightarrow \mathbb {R}$

be a rational function. Prove that ${}F$ is a polynomial if and only if there is a higher derivative such that

${}F^{(n)}=0$.

Create a solution