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A plane begins its takeoff at 2:00 p.m. on a 2170-mile flight. After 5.1 hours, the plane arrives at its destination. Explain why there are at least two times during the flight when the speed of the plane is 200 miles per hour. STEP 1: 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) = = 2170 STEP 2: The Mean Value Theorem says that there exists a time to, 2170- S '(to) = v(to) STEP 3: Now v(0) = <-0 , and v(5.1) = least two times during the flight when the speed was 200 miles per hour. < to < and since v(to) = , such that the following is true. (Round your answer to two decimal places.) we have 0 < 200 < v(to). Thus, we can apply the Intermediate Value Theorem to the velocity function on the intervals [0, to] and [to ] to see that there are at
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