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Math Help - Local Minimums and Maximums

  1. #1
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    Local Minimums and Maximums

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

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


    <br />
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 x \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
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    Sep 2008
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    Champaign, Illinois
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    1,163
     \in means is contained in. So  x\in [-13,14] reads  x is contained in the interval  [-13,14] .


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