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Derivatives : Rate-of-Change Word Problem

For several weeks , campus security has been recording the speed of trafic flowing past a certain intersection on campus. The data suggests that between 1:00 and 6:00 pm on a normal weekday, the speed of the traffic at the intersection is approximately S(t)=t^3-10.5t^2+30t+20 miles per hour, where t is the number of hours past noon. At what time between 1:00 and 6:00 pm is the traffic moving the fastest?

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Solution. since S(t)=t^3-10.5t^2+30t+20 , we have

Solution Summary

Derivatives are used to find a maximum value. The solution is detailed and well presented.