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A particle moves on a horizontal line as described by the equation s = t 3 −12t + 3 . a. When is the particle changing directions? b. When is the particle moving to the right and when is it moving to the left?

Mathematics
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The particle changes direction when the velocity changes sign, so you would have to find out what specific times t, the function's velocity goes from neg->pos or pos->neg.
You can set the v=0
Does this make sense?

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Other answers:

I already did it. But I was thinking about what to do with -2. I came up with 3(t-2)(t+2)=0 t=2, what shall I do with -2? There's no negative time -.-
Yup, if you can't have -2 but 2 is also an answer, the answer will be.....?
2?
Yup. I haven't done the problem, but if that was your point of confusion, yes, if you have something for t that doesn't make sense (such as when t=0, or neg.) you can disregard it and only use the positive answer.
So that's it. I can do it now. Thanks

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