(i) Prove or disprove that a continuous and oneone function dened on a closed interval is monotone.| (ii) Suppose f: [0, 2] > R is a real valued function such that f and f' are differentiable on [0, 2]. Prove that: if f(0) = 1,f(1) = 2 and f(2) = 3, then (a) there exist two distinct u, v E (0, 2) such that f'(u) = f'(v) = 1, and (b) there exists w 6 (0,2) such that f\"(w) = 0. (iii) Let R>0 be the set of positive real numbers, X be a nonempty bounded from below set of real numbers and 7\" = ian. Show that {[r, r | E)}6R>O is a cover for X