  This paper originated as an appendix to the paper "Topology and Geometry of
the Berkovich Ramification Locus for Rational Functions, II" by Xander Faber
arXiv:1104.0943v2 [math.NT]. It may however be read independently. We prove a
variant of Alain Robert's p-adic Rolle theorem, via the theory of the radius of
convergence of p-adic connections and the theory of semistable reduction of
p-adic curves. We carefully compare the present author's notion [Inv. Math. 182
(2010)] of radius of convergence, of a connection on a p-adic curve X,
normalized by the choice of a semistable model of X, with Kedlaya's intrinsic
generic radius of convergence of a differential module [Def. 9.4.7 in p-adic
Differential Equations, Cambridge Studies in Adv. Math., vol. 125 (2010)].
