Examine if Rolle’s theorem is applicable to any of the following functions. Can you say something about the converse of Rolle’s theorem from these examples?

(i) f (x) = [x] for x ∈ [5, 9]

(ii) f (x) = [x] for x ∈ [– 2, 2]

(iii) f (x) = x 2 – 1 for x ∈ [1, 2]