Given the position function, s of t equals negative t cubed divided by 3 plus 13 times t squared divided by 2 minus 30 times t, between t = 0 and t = 9, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right.

3 < t < 9
5 < t < 9
The particle never moves to the right.
The particle always moves to the right. <- This is my answer

1 answer

what's with all the words?

s(t) = -t^3/3 + 13t^2/2 - 30t
when the particle is mofing to the right, s(t) is increasing, so ds/dt > 0

-t^2 + 13t - 30 > 0
3 < t < 10

Since our domain is 0<t<9, our interval is thus

3<t<9