Aparticle starts at time t=0 and moves along a number line so that its position, at time t is greater than or equal to zero, is given by x(t)= (t-2)(t-6)^3. the particle is moving to the left

at t=0
 x(0) = (-2)* (-6)^3= 432.
nitial position. At t=2, x(2)=0.
 We can see that our particle is moving towards the left on the axis (by getting from 432 to 0
At t>2 and t<6, x(t) <0.
Our particle is still going left - now beyond the y axis
. At t=6, x(6) = 0
 since we were left from the y axis (because we were going negative earlier) that means the particle took a right turn this time.
. At t>6, x(t)>0 the particle is still going right and will keep on going to infinity.
 6 seconds.is answer hope this helps

Do the inverse operation