5. Zeros of derivatives

Problem 5.1.
[S. Edwards] Let $p\in\mathbb{R}[x]$, $\deg(p)=n>2$. There are at least $n1$ points of extreme curvature $\kappa(p)$ ( more generally where $\kappa'(p)=0$ ) [MR2104693]. 
Problem 5.2.
[A. Sokal] What are the zero spacing effects of higher order differential operators on functions which belong to $\mathcal{L}\text{}\mathcal{P}$?
Cite this as: AimPL: Stability and hyperbolicity, available at http://aimpl.org/hyperbolicpoly.