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?
Solution. since S(t)=t^3-10.5t^2+30t+20 , we have
Derivatives are used to find a maximum value. The solution is detailed and well presented.