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Math Help - Interval Problem

  1. #1
    s3a
    s3a is offline
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    Interval Problem

    I highlighted what I'm having trouble with on the 4.pdf file. Even with the graph of my graphing software, I would put the exact same notation (used graphing software after doing my work to see where I was wrong but I seem to be right according to my software). I attached my work as the mywork.pdf file as well as the graph of the original function (f(x)=(4x^2)/(x^2 - 9)) as Graph.png.

    The intervals I'm suggesting are:

    Increasing on:
    Decreasing on:

    Why am I wrong?

    Any help would be greatly appreciated!
    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Interval Problem-graph.png  
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  2. #2
    Member Em Yeu Anh's Avatar
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    Looks correct to me. Hmm. 0 is included in both increasing and decreasing intervals, perhaps that's the error?
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  3. #3
    Super Member Bacterius's Avatar
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    Yes. The 0 is neither increasing nor decreasing, so it shouldn't be in neither interval. It should be :

    (-\infty ; -3) \cup (-3 ; 0) and (0 ; 3) \cup (3 ; +\infty)

    Do not forget a function cannot be increasing and decreasing at the same point, because that would mean that the derivative of the function at this point has two different signs, which is only possible with number 0, however this result has special meaning, it means that the function is constant on that interval.
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