A particle moves along a line so that at any time t its position is given by x(t)=2(pi)t + cos(2(pi)t)a)what are all values of t in which the object is at rest from 0 to 3b)what is the max velocity?

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Nicole -a) x(t) is the position function so the first derivative with respect to t will give you the velocity function or v(t).  Solve v(t) = 0 over the interval [0,3] and this will tell you when the velocity is zero or when the object is at rest, agree?b) If you graph v(t), the max velocity occurs at the peak or highest value of the curve over [0,3].  Algebraically, take the derivative of v(t) which is acceleration or a(t) and solve for a(t) = 0.  Check to see if your solution is a maximum over [0,3] and don't forget to check the endpoints t=0 and t=3 evaluated using v(t).Hope that helps