True/False: Determine whether each of the statements that follow is true or false. If the statement is true, explain why. If the statement is false, provide a counterexample. (a) If f (x) is continuous on the open interval (0,5), then f (x) is continuous at every point of in (0,5) (b) If f (x) is continuous on the interval (2,4), then f (x) must have a maximum value and minimum value on (2,4). (c) If f(3) = -5 and f(5) = -2, then there must be a value c at which f(c) =-3 (d) If f(0) = -2 and f(4) =3, then f(x) there must have a root somewhere in (0,4). (e) If f(0) = f(6) =0 and f (2) > 0, then f (x) is positive on the entire interval (0,6)