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). 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?

Question

agreene · Answer

start by solving for 0=(4t-1)(t-1)
so you know when directional changes occur. Positive is Right, Negative is Left. 
Then find the velocity and maximize it while it's negative for the second part.