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Math Help - Interval of increase/decrease

  1. #1
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    Interval of increase/decrease

    Find the interval of increase/decrease of f = x^(1/7) (x+8)

    I started to find f' = x^(1/7) + (x+8) (1/7 x^(-6/7)) But when I try to simplify and solve for x, everything gets strange and I know that I am not doing it right. Can you show me the steps, please? Thanks.
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  2. #2
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    Quote Originally Posted by Maziana View Post
    Find the interval of increase/decrease of f = x^(1/7) (x+8)

    I started to find f' = x^(1/7) + (x+8) (1/7 x^(-6/7)) But when I try to simplify and solve for x, everything gets strange and I know that I am not doing it right. Can you show me the steps, please? Thanks.
    Try multiplying through first. I think that will make it a little easier.

    f=x^{8/7} + 8x^{1/7}
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  3. #3
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    f' = x^(8/7) + 8x^(1/7)

    8/7 x^(1/7) + 8/7 x^(-6/7)

    x^(1/7) = -x^(-6/7)

    x = -x^-6

    x = -1/x^6

    x^7 = -1

    x = -1

    Thanks.
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  4. #4
    Member WhoCares357's Avatar
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    Quote Originally Posted by Maziana View Post
    f'' = x^(8/7) + 8x^(1/7)

    8/7 x^(1/7) + 8/7 x^(-6/7)

    x^(1/7) = -x^(-6/7)

    x = -x^-6

    x = -1/x^6

    x^7 = -1

    x = -1

    Thanks.
    Wait, so the first equation is the second derivative? I thought it was the original function.

    Edit: But you are right.
    x=-1 is one of the zeroes. The other zero is at x=0. However, if you remember the first step after taking the derivative is finding the domain. In this case x <> 0, because 0 in the denominator would be undefined.

    Now just test before and after -1 and before and after 0 to find rise/fall.
    Last edited by WhoCares357; October 28th 2009 at 03:17 PM.
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