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Math Help - second differentiation problem

  1. #1
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    second differentiation problem

    Hello, I need to establish if:
    t(tan(t)) is accelerating or deccelerating at t=pi/4

    My attempt is:

    1. differentiate to get velocity function:
    tant + tsec^2t

    2. differentiate again to find acceleration function
    1/cos^2t + sec^2t + t(2sint/cos^3t)

    3. Now I plug in pi/4 and get an acceleration of 7.142.

    Hopefully I have the above all correct ?
    Do I now simply use a pair of test points on either side of pi/4 to establish if the acceleration is increasing or decreasing ?
    or does the fact that the acceleration is positive tell me that it is accelerating rather than deccelerating ?

    Thanks for any help.
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  2. #2
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    Re: second differentiation problem

    Quote Originally Posted by fran1942 View Post
    Hello, I need to establish if:
    t(tan(t)) is accelerating or deccelerating at t=pi/4

    My attempt is:

    1. differentiate to get velocity function:
    tant + tsec^2t

    2. differentiate again to find acceleration function
    1/cos^2t + sec^2t + t(2sint/cos^3t)

    3. Now I plug in pi/4 and get an acceleration of 7.142.

    Hopefully I have the above all correct ?
    Do I now simply use a pair of test points on either side of pi/4 to establish if the acceleration is increasing or decreasing ?
    or does the fact that the acceleration is positive tell me that it is accelerating rather than deccelerating ?

    Thanks for any help.
    Looks to be correct. And it's the fact that the acceleration is positive that tells you the function is accelerating rather than decelerating.
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