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Thread: Local Minimums and Maximums

  1. #1
    Member
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    Local Minimums and Maximums

    I'm not really understanding how to do this problem.

    For $\displaystyle x$ $\displaystyle \in [-13,14]$ the function $\displaystyle f$ is defined by


    $\displaystyle
    f(x)=x^7(x+6)^2$

    On Which two intervals is the function increasing?
    ___to___
    and
    ___to___
    Find the region in which the function is positive?
    ___to___
    Where does the function achieve it's minimum?
    ___
    My first step is to take the derivative and find the critical numbers.

    But what I don't get is:

    What does this mean?
    For $\displaystyle x$ $\displaystyle \in [-13,14]$
    Is a different way of saying find where the function is increasing?
    Find the region in which the function is positive?
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  2. #2
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
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    Champaign, Illinois
    Posts
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    $\displaystyle \in $ means is contained in. So $\displaystyle x\in [-13,14] $ reads $\displaystyle x $ is contained in the interval $\displaystyle [-13,14] $.


    $\displaystyle f(x) $ positive doesn't mean $\displaystyle f(x) $ is increasing.
    $\displaystyle f(x)=\cos(x) $ on the interval $\displaystyle (0,\frac{\pi}{2}) $ is positive but decreasing.
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