Rolle's Theorem, "Let f be a continuous function on [a,b] that
is differentiable on (a,b) and such that f(a)=f(b). Then there
exists at least one point c on (a,b) such that f'(c)=0."
Rolle's Theorem requires three conditions be satisified.
(a) What are these three conditions?
(b) Find three functions that satisfy exactly two of these three
conditions, but for which the conclusion of Rolle's theorem does
not follow, i.e., there is no point c in (a,b) such that f'(c)=0.
Each...