A particle moves on a straight line so that its position \( s \) (in miles) at time \( t \) (in hours) is given by \( s = (4t-1)(t-1)^2 \). When is the particle moving to the right, when to the left, and when does it change direction? When the particle is moving to the left, what is the maximum speed that it achieves?
calculuskinematicsrectilinear-motionvelocityaccelerationspeedproduct-ruleoptimizationsecond-derivative-testcritical-pointsintervals-of-increase-and-decreasepolynomial-differentiation
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