A particle moves along a linear path (left/right) and its position, relative to its starting location is given by the function s(t)=13t^3−2t^2+3t , t≥0.

Question

A particle moves along a linear path (left/right) and its position, relative to its starting location is given by the function s(t)=13t^3−2t^2+3t , t≥0. 
a) Determine the particle's velocity and acceleration at any time t.
b) When does the particle change direction? You must prove there is a change of direction.

oobleck · Answer

it can't change direction without stopping for an instant. velocity is ds/dt, so when does s'=0?