We consider the function $f : \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \mathrm{e}^{-\frac{1}{2}x^{2}}$ for all $x \in \mathbb{R}$. Show that there exists a real number $M > 0$ such that $f$ is an $M$-Lipschitz function.
We consider the function $f : \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \mathrm{e}^{-\frac{1}{2}x^{2}}$ for all $x \in \mathbb{R}$.
Show that there exists a real number $M > 0$ such that $f$ is an $M$-Lipschitz function.