Question

The velocity for a particle traveling along the x-axis, measured in feet/second, is represented by v(t)=−2((t−3)^2)(t+1)(t−6). At what time(s) does the particle change direction?
Group of answer choices

A. t=1,6
B. t=3,6
C. t=1,3,6
D. t=6

Answer 1

it changes direction when the velocity goes to zero and changes sign, right?
It is clear that v=0 at t=-1,3,6
Since t=3 is a double root, v does not change sign there, so t = -1,6 are the only solutions.

You have a typo, either in the question or the answers.

See the graph at

https://www.wolframalpha.com/input/?i=%E2%88%922%28%28t%E2%88%923%29%5E2%29%28t%2B1%29%28t%E2%88%926%29