While time $t0$ a particle moves along a straight line. Its position at time $t$ is given by

$s(t)=2t^3-21t^{2}72t,t0$

where $s$ is measured in feet and $t$ in seconds.

$($A$)$ Use $$ to indicate the time interval or union of time intervals when the particle is moving forward and backward.

Forward:

Backward: $$ v

$($B$)$ Use $$ to indicate the time interval$($s$)$ when the particle is speeding up and slowing down.

Speeding up: $$

Slowing down:

$("$Speeding up$"$ and "slowing down" refer to changes in speed, the absolute value of velocity.$)$

Note: You can earn partial credit on this problem.