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Which of the following are conditions for the Mean Value Theorem? 0 For the Mean Value Theorem to apply, f(x) needs to be continuous on an open interval (a, b). o For the Mean Value Theorem to apply, f(x) needs to be continuous on a closed interval [a, b]. O For the Mean Value Theorem to apply, f(x) needs to be a function on the open interval (a, b)- O For the Mean Value Theorem to apply, f(x) needs to be differentiable on a open interval (a, b). Forf(x) = 3 lxl, does the Mean Value Theorem apply on the interval [-2. 2] and why? 0 The Mean Value Theorem does not apply because x) is not continuous on the closed interval [-2. 2]. O The Mean Value Theorem applies because. flat) is differentiable on the closed interval [-2. 2]. O The Mean Value Theorem applies because x) is continuous on [-2 2]. O The Mean Value Theorem does not apply because x) is not differentiable on the open interval (-2, 2}. For f(x) = 2x- - x + 1, find all the values of c on the interval [0, 1] that satisfy the Mean Value Theorem. O C = -0.5 O C = 0.375 O C = 0.5 O C = 0.68For f(x) = - Vx + 2, find all the values of c on the interval [2, 7] that satisfy the Mean Value Theorem. O C=-4.75 O C=-4.25 O C = 4.25 O C= 4.75Let f (x) = x - 4x. Using Rolle's Theorem, what are all the values c in the interval [-2, 2] such that f '(c) = 0? O c = 1 and c = 2 OC= : 2V/3 3 O c = 0.5 and c = -0.5 O c= +2V3A ball is thrown up into the air at time t = 0, then it comes back down and at time t = 1 it is caught. Can Fiolle'a Theorem be applied to show that at some point between t = 0 and t = 1. the ball has achieved a maximum andior minimum speed? 0 The conditions of Ftolle's Theorem are not met and Ficlle's Theorem does not state that you can find min or max points. 0 The conditions of Ftolle's Theorem are met and Rolle's Theorem does state that you can find min or max points. 0 The conditions of Ftolle's Theorem are not met and Ftolle's Theorem does state that you can find min or rnax points. 0 The conditions of Ftolle's Theorem are met and Rolle's Theorem does not state that you can find min or max points. Iff (t) = -12 - 7t + 3 describes the distance that a ball has traveled in meters/sec, what is the average rate of change of the ball between t = 1 second and t = 2 seconds? O Average rate of change between t = 1 and t = 2 is 10 m/s. O Average rate of change between t = 1 and t = 2 is -10 m/s. O Average rate of change between t = 1 and t = 2 is -20 m/s. O Average rate of change between t = 1 and t = 2 is 20 m/s.If f (t) = 90 + 10 sin(t) describes the length of an oscillating spring in m/s, what is the instantaneous rate of change of the spring at time t = n sec? O 10 m/s O 1 m/s 0 0 m/s O -10 m/sLet k = 432: . wheret is time measured in seconds. What is the instantaneous rate of change at 1 = 1 second? O 1.03 D 1 C! 0.4 (:3 l.08 The roller coaster rides at Math Games are all shaped like trigonometric functions. Dan goes on the "sine" ride and his height in meters is measured by h(t) = 5sin(t) + 10. At t=n sec, what is Dan's instantaneous rate of change? O 10IT m/s O -5 m/s O -10 m/s O - 10TT m/s