Rolle's theorem requires three conditions be satisfied:

i. f is continuous on [a,b]

ii. f is differentiable on (a,b), and

iii. f(a)=f(b)

Find three functions that satisfy exactly two of these three conditions, but for which the conclusion of Rolle's theorem does not follow. That is, there is no point c element of (a,b) such that f](c) = o