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Math Help - Concavity

  1. #1
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    Concavity

    I tried taking the derivative and it is an absolute mess, so I thought there had to be an easier way. It says find the interval on which the integral of y=1/(1+t+t^2) from 0 to x is concave upward. Is there an easier way than taking the derivative of that?
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  2. #2
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    Quote Originally Posted by sfgiants13 View Post
    I tried taking the derivative and it is an absolute mess, so I thought there had to be an easier way. It says find the interval on which the integral of y=1/(1+t+t^2) from 0 to x is concave upward. Is there an easier way than taking the derivative of that?

    raise the whole bottom to the top so that it becomes raised to the -1.

    then do chainrule, this should work.
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  3. #3
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    I did that and I may have got it...I got all values of x, and got the derivative of that to be 1/2sqrt[1+t+t^2]. Can anyone confirm this?
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  4. #4
    Super Member 11rdc11's Avatar
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    -(1+t+t^2)^{-2}(1+2t)
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  5. #5
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    Quote Originally Posted by sfgiants13 View Post
    I did that and I may have got it...I got all values of x, and got the derivative of that to be 1/2sqrt[1+t+t^2]. Can anyone confirm this?

    you forgot a key part, you need to multiply by derivative of the inside. So no not really.
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