Does the cyclist ever turn around

| August 31, 2017

Question
A cyclist is traveling along a straight road near her friend’s house for one hour with velocity given by v(t) = (144t)(3t − 1)(t − 1) where t is measured in hours, v(t) is measured in kilometers per hour, and positive velocities take her towards her friend’s house. She starts out at marker which is 5 kilometers from her friend’s house.
(a) Does the cyclist ever turn around?
(b) When is she going the fastest? How fast is she going? Is she headed towards her friend’s house or away at that time?
(c) When is she closest to her friend’s house? How close to her friend’s house does she get?
(d) When is she farthest from her friend’s house? How far from her friend’s house is she then?

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