Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a) = f(b). (Select all that apply.) f(x) = 1 - |x - 1|, [0, 2] There are points on the interval (a, b) where f is not differentiable. f(a) does not equal f(b) for all possible values of a and b in the interval [0, 2]. There are points on the interval [a, b] where f is not continuous. Of'(a) does not equal f'(b) for any values in the interval [0, 2]. None of these.Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two x-intercepts. f(x) = -2xx+3 ( x, y) = (smaller x-value) ( x, y ) = (larger x-value) Find a value of x such that f'(x) = 0. X =Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = (x - 1)(x - 3)(x - 8), [1, 8] Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. O No, because f is not differentiable in the open interval (a, b). No, because f(a) # f(b). X 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 = XDetermine whether Rolle's Theorem can be applied to fan the closed interval [a, b]. (Select all that apply.) f(x) = )(2/3 5, [27, 27] [:1 Yes, Rolle's Theorem can be applied. D No, because fis not continuous on the closed interval [a, b]. C] No, because f is not differentiable in the open interval (a, b). C] No, because f(a) at f(b). [f 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: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = X2 - 2x - 15 [-3, 5] X + 8 O Yes, Rolle's Theorem can be applied. O No, because f is not continuous on the closed interval [a, b]. O No, because f is not differentiable in the open interval (a, b). O No, because f(a) # f(b). 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 =Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 5 cos xx, [0, 2] O Yes, Rolle's Theorem can be applied. O No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). O No, because f(a) # f(b). 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=