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Math Help - optimzation problem #2

  1. #1
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    optimzation problem #2

    A sociologist determines that a foreign-language student has learned N(t)=20t-t^2 vocabulary terms after t hours of uninterrupted study.

    What is the maxmimum rate in terms per hour at which the student is learning?

    Ok.. this is what I did, but the back of the book has a different answer than my final answer.

    My answer: 100
    Back of book: 20


    My work:
    N'(t)=20-2t
    0=20-2t
    10=t

    N(10)=10(20)-10^2
    =100

    So, what did I do wrong?
    Last edited by mr fantastic; August 12th 2009 at 04:32 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    A sociologist determines that a foreign-language student has learned N(t)=20t-t^2 vocabulary terms after t hours of uninterrupted study.

    What is the maxmimum rate in terms per hour at which the student is learning?

    Ok.. this is what I did, but the back of the book has a different answer than my final answer.

    My answer: 100
    Back of book: 20


    My work:
    N'(t)=20-2t
    0=20-2t
    10=t

    N(10)=10(20)-10^2
    =100

    So, what did I do wrong?
    you've been asked to find the maximum for N'(t) , not N(t) ...

    N'(t) = 20-2t

    N'(t) is a maximum when t = 0

    N'(0) = 20
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