The displacement of a precision positioning stage along a straight rail is modelled by s=t4−8t3+16t2s=t^4-8t^3+16t^2s=t4−8t3+16t2 metres for 0≤t≤60\leq t\leq60≤t≤6.
Find all times when the particle is instantaneously at rest.
Classify each stationary position as a local maximum or a local minimum of displacement.
Find the greatest distance of the particle from the origin in the interval.