The position of a particle is given by S(t) = t^3 - 6t^2 + 2 when does the particle change direction?Step by step process

The particle is moving such that its position is given by
S(t) = t^3 - 6t^2 + 2.

When the particle changes direction
the velocity changes sign.

Velocity is given by V(t) =
S'(t) = 3t^2 - 12t

3t^2 - 12t =
0

=> 3t = 12

=>
t = 12/3

=> t =
4

Before t = 4, the velocity of the particle is negative,
after t = 4 the velocity of the particle becomes
positive.

At t = 4, the particle changes
direction.