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Unformatted text preview: Section 2.4 Average Rate of Change of a Function Suppose you take a car trip and record the distance that you travel every few minutes. The distance s you have traveled is a function of the time t : s ( t ) = total distance traveled at time t We graph the function s as shown in the Figure below. The graph shows that you have traveled a total of 50 miles after 1 hour, 75 miles after 2 hours, 140 miles after 3 hours, and so on. To find your average speed between any two points on the trip, we divide the distance traveled by the time elapsed. Lets calculate your average speed between 1:00 P.M. and 4:00 P.M. The time elapsed is 4- 1 = 3 hours. To find the distance you traveled, we subtract the distance at 1:00 P.M. from the distance at 4:00 P.M., that is, 200- 50 = 150 mi. Thus, your average speed is average speed = distance traveled time elapsed = 150 mi 3 h = 50 mi/h The average speed we have just calculated can be expressed using function notation: average speed = s (4)- s (1) 4- 1 =...
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