# Math Help - real analysis

1. ## real analysis

Suppose $f$ is infinitely differentiable on $\mathbb{R}$.

(a) If $\left|{f(x)\right|\leq 1 + \left|x\right|^m$ for some $m\in \mathbb {N},$ and for all $x\in\mathbb{R},$then $f(x)$ is a polynomial.

2. This is not true: take $f(x)=\sin(x)$ and note the statement is true for any $m\in\mathbb{N}$.