(13) (a) Let f : [a, b] - R be a continuous function. For x E (a, b) define [Df(x)], := MER |3(xn),=] C (x, b), such that lim Xn = x and lim f (x) - f(xn) = MS 11-+00 1-+00 x - Xn Prove that for any x E (a, b), [D (x)], is a closed interval. (Possibly unbounded or a singleton set). Carefully note that for every n, X E (x, b) (the r is for right). (b) Show (by example) that the same is not true for Do(x) := MER (xn),=] C [a, b], such that lim X, = x and lim f (x) - f(xn) = M 1-+00 17-+00 x - Xn