While time $t0$ a particle moves along a straight line. Its

position $at$ time $tis$ given $by$

$s(t)=2t^3-24t^2+90t,t0$

where $sis$ measured $in$ feet and $tin$ seconds.

$(A)$ Use interval notation $to$ indicate the time interval $or$

union $of$ time intervals when the particle $is$ moving forward

and backward.

Forward:

Backward:

$(B)$ Use interval notation $to$ indicate the time interval$(s)$

when the particle $is$ speeding $up$ and slowing down.

Speeding $up$:

Slowing down:

$("Speedingup"$ and "slowing down" refer $to$ changes $in$

speed, the $absolute$ value $of$ velocity.$)$

$If$ your interval starts $at0,$ use a square bracket $to$ include,

rather than exclude, $0i.e.[0,a)$