For Exercises 33–36, use the distance function s(t) = 16t2 discussed on page 159 and in Example 6. Recall that this function relates the distance s(t) and the time t for a freely falling object (neglecting air resistance). The time t is measured in seconds, with t = 0 corresponding to the instant that the object begins to fall; the distance s(t) is in feet.
(a) Find the average velocity over each of the following time intervals: [2, 3], [3, 4], and [2, 4].
(b) Let a, b, and c denote the three average velocities that you computed in part (a), in the order given. Is it true that the arithmetical average of a and b is c?
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