Determine whether Rolle\'s Theorem can be applied to F on the closed interval [a

Question

Determine whether Rolle's Theorem can be applied to F on the closed interval [a, 6]. (Select all that apply.) f(x) = (x - 1)(x - 3)(x - 5), [1, 5] Yes. No, because f is not continuous on the closed interval [a, b]. No, because F is not differentiable in the open interval (a, b). 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 HA.) c = Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 19 - x, [-6, 19] Yes, the Mean Value Theorem can be applied. No, f is not continuous on [a, b]. No, f is not differentiable on (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = f(b) - f(a)/b - a. (Enter your ansv/ers as a comma-separated list. If the Mean Value 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) = 12x/pi - 8(sin(x))2, [0, pi/6] Yes. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). 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) = x-4/5 - 6, [-32, 32] Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). 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 = A plane begins its takeoff at 2:00 p.m. on a 1799-mile flight. After 4.1 hours, the plane arrives at its destination. Explain why there are at least tv/o times during the flight when the speed of the plane is 100 miles per hour. STEP l:Let S(t) be the position of the plane. Let t = 0 correspond to 2 p.m., and fill in the following values. s(0) = s = 1799 STEP 2:The Mean Value Theorem says that there exists a time t0,

Explanation / Answer

1. Yes

c=4.15470,1.84529

2.Yes

c= 12.75

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