The following rational function models the speed V (t), in miles per hour, of a dragster t seconds since it starts its quarter-mile run:
V (t) = 340tt2 + 3
(a) Respond to the claim that during the first 4 seconds of the dragster's run, it attains a maximum speed and then begins to slow down. Is the claim true or false? Support your answer with mathematics.
(b) What is the absolute maximum speed of the dragster on the interval during the first 4 seconds and at what time in the first 4 seconds of its run does it occur? Round you maximum speed to two decimal places.