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Math Help - Local Max and Interval Problem help please

  1. #1
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    Unhappy Local Max and Interval Problem help please

    The function f(x)=6x^3-27x^2-72x+6
    is decreasing on the interval (-1,4).
    It is increasing on the interval ( -INF, -1) and the interval (4, INF).
    The function has a local maximum at _______.

    i had a hard time finding the local maximum. so what is the answer. i will gratefully appreciated.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    local maximum at (1-e,1+e)
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  3. #3
    MHF Contributor
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    Quote Originally Posted by jpratt View Post
    The function f(x)=6x^3-27x^2-72x+6
    is decreasing on the interval (-1,4).
    It is increasing on the interval ( -INF, -1) and the interval (4, INF).
    The function has a local maximum at _______.

    i had a hard time finding the local maximum. so what is the answer. i will gratefully appreciated.
    increasing to x = -1, decreasing to x = 4, increasing as x -> infinity

    make a sketch ... where will f(x) have a relative maximum?
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