Consider the following function and closed interval. f(x) = (x - 1)(x - 5)(x - 9), (1,9] Is f continuous on the closed interval [1, 91? O Yes O No If f is differentiable on the open interval (1,9), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f'(x) = Find f(1) and (9). f(1) = f(9) = Determine whether Rolle's Theorem can be applied to fon the closed interval [a, b]. a) Yes, Rolle's Theorem can be applied.
b) No, because fis not continuous on the closed interval [a, b].
c) No, because fis not differentiable in the open interval (a, b).
d) No, because fa) f(b).
e) If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) C=