The function $\small{s(t)}$ describes the position of a particle moving along a coordinate line, where $\small{s}$ is in feet and $\small{t}$ is in seconds. $$\small{s(t) = t^{3}-6t^{2}+9t+6, \qquad t \ge 0}$$

(a) Find the velocity and acceleration functions.

$\small{v(t)}$:
$\small{a(t)}$:

(b) Over what interval(s) is the particle moving in the positive direction? Use inf to represent $\small{\infty}$, and U for the union of sets.

Interval:

(c) Over what interval(s) is the particle moving in the negative direction? Use inf to represent $\small{\infty}$, and U for the union of sets.

Interval:

(d) Over what interval(s) does the particle have positive acceleration? Use inf to represent $\small{\infty}$, and U for the union of sets.

Interval:

(e) Over what interval(s) does the particle have negative acceleration? Use inf to represent $\small{\infty}$, and U for the union of sets.

Interval:

(f) Over what interval is the particle speeding up? Slowing down? Use inf to represent $\small{\infty}$, and U for the union of sets.

Speeding up:
Slowing down: