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Math Help - Interval when moving to right and left?

  1. #1
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    Interval when moving to right and left?

    Determine the time interval on which the point is moving to the right and to the left.

    Point P is moving along the x axis so that its position x at time t is given by x=3t^3-4t+1

    So I determined the velocity and accleration equations:

    v(t) = 3t^2-4
    a(t) = 6t

    But I have no clue how to determine what time intervals which the point is moving to the right or to the left?
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  2. #2
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    Re: Interval when moving to right and left?

    If x(t) = 3t^3 - 4t + 1, then v(t) = 9t^2 - 4.

    The points is moving right when v(t) > 0 and left when v(t) < 0.
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  3. #3
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    Re: Interval when moving to right and left?

    Oops the first function before velocity was actually supposed to be x = t^3 -4t +1

    But how would I determine when v(t) > 0 and when v(t) < 0?
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  4. #4
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    Re: Interval when moving to right and left?

    Quote Originally Posted by kmjt View Post
    But how would I determine when v(t) > 0 and when v(t) < 0?
    Here is a tutorial on solving quadratic inequalities.
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