Editing Rolle's theorem (section)

===Remarks===
* If {{mvar|f}} is convex or concave, then the right- and left-hand derivatives exist at every inner point, hence the above limits exist and are real numbers.
* This generalized version of the theorem is sufficient to prove [[Convex function|convexity]] when the one-sided derivatives are [[monotonically increasing]]:<ref>{{citation |last=Artin |first=Emil |author-link=Emil Artin |translator-first= Michael |translator-last= Butler |title=The Gamma Function |orig-year=1931 |year=1964 |publisher=[[Henry Holt and Company|Holt, Rinehart and Winston]] |pages=3–4}}.</ref> <math display="block">f'(x^-) \le f'(x^+) \le f'(y^-),\quad x < y.</math>