Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a function of class $C^{\infty}$ with compact support. For all $n \in \mathbb{N}$, we set
$$M_{n} = \sup_{x \in \mathbb{R}} \left|f^{(n)}(x)\right| = \left\|f^{(n)}\right\|_{\infty}$$
In this part we assume that $f$ is not identically zero.
Deduce that for all $B > 0$ we have
$$\frac{M_{n}}{B^{n} n!} \underset{n \rightarrow \infty}{\longrightarrow} +\infty$$