A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function: s(t)=6t^3+72t^2
What is the average speed of the train (average rate of change) between 2 and 5 hours?
What is the velocity (instantaneous rate of change) of the train at exactly 2.5 hours into the trip?
What is the maximum velocity attained by the train? Please justify.