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...

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 ∈ (a, b) such that f ′ (c) = 0.