A bicycle rider rides from home along a highway and back along the same road in such a way that her distance from home at time t is given by X = t**4 - 8t**3 + 16 t**2 where t is in hours and x in kilometers. Here X is the function of time as shown.
(a) After how many hours does the rider get home?
(b) How far from home in kilometers does the rider go?
(c) What is the average speed of the rider in terms of kilometers per hour?
(d) After how many hours does the rider's maximum speed occur?