5. Use the definition of the derivative of a function to prove the following: (i) That is, show that d dx dx [ ]] =-2-2 (ii) d 1 dx That is, show that dx [x 1/2 ] = $20-1/2 6. Prove the converse of Lemma 8.8. That is, let A be a real number and suppose: flat h) - f(a) = Ah + h . E(h) for any h # 0, with lime(h) = 0. Show that f is differentiable at * = a h+0 and that f'(a) = A. 7. (Bonus) Let f be a continuous function on a closed bounded interval [a, b]. Show that the range of f is also a closed, bounded interval. Here the range of f is defined as the set {f(x) | a