Let s=30/(t^2+12) be the position function of a particle moving along a coordinate line, where s is in feet and t is in seconds.
(a) Find the maximum speed of the particle for t>=0 . If appropriate, leave your answer in radical form.
Speed (ft/sec): ?
(b) Find the direction of the particle when it has its maximum speed.

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part a) take the derivative of s with respect to "t" and then set it equal to zero to find the min and max points-(thats where the slope is zero or constant).
speed = the absolute value of velocity which is what your finding in part a-
velocity= change of position/ change of time
take your value of time that you find in part a and plug it into your derivative equation to find the speed at the particle's max/min.
part b) use your derivative in part a to tell whether the function is increasing or decreasing. If the function is decreasing, your velocity is slowing down; if the function is increasing your velocity is speeding up-so your either going one way or the other on your coordinate line.
hope this helps you.

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