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Given the position function, s of t equals t cubed divided by 3 minus 12 times t squared divided by 2 plus 36 times t, between t = 0 and t = 15, 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.
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\[s(t)= \frac{ t^3 }{ 3 }-\frac{ 12t^2 }{ 2 }+36t\]
a.0<t<6 b.5<t<15 c.t>15 d. The particle always moves to the right
@mathstudent55 @Mehek14
@Maharot
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