(a) Decide whether the following statements are true; briefly justify your an- swers (you may quote any theorem from the lectures). (i) Every continuous function f : [-9, 11] → R has a minimum. (ii) Every continuous function f : (-5, 1] → R has a maximum. (iii) Every continuous function f : (−1, 1] → R has a supremum. (iv) The set [0,8) has a supremum but no maximum. (b) Let f R R be a differentiable function. Let a, b = R be such that a