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Math Help - Finding locations of absolute extrema

  1. #1
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    Finding locations of absolute extrema

    Trying to review for my test next week and this is an example problem that I have a feeling will be on the test yet I am somewhat lost on how to solve. Thanks in advance for the help!


    Find the locations of all absolute extrema for the function....

    f(x) = 2x^3 + 3x^2 -36x +12 with the domain [ -2, 4 ]


    I know I'm supposed to use the first derivative test correct?

    f'(x) = 6x^2 + 6x - 36
    0 = 6x^2 + 6x - 36

    Could someone please solve it from here(assuming I am right so far)?
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  2. #2
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    Quote Originally Posted by Mathamateur View Post
    Trying to review for my test next week and this is an example problem that I have a feeling will be on the test yet I am somewhat lost on how to solve. Thanks in advance for the help!


    Find the locations of all absolute extrema for the function....

    f(x) = 2x^3 + 3x^2 -36x +12 with the domain [ -2, 4 ]


    I know I'm supposed to use the first derivative test correct?

    f'(x) = 6x^2 + 6x - 36
    0 = 6x^2 + 6x - 36

    Could someone please solve it from here(assuming I am right so far)?
    Three points:
    1) You are looking for "relative" extrema within the interval. This function has no absolute extrema.

    2) Don't forget the end points of the domain!

    3) Dude! This is a quadratic. If you can't figure out how to solve it, just use the quadratic formula. So saying:
    6x^2 + 6x - 36 = 0

    6(x^2 + x - 6) = 0

    x^2 + x - 6 = 0

    (x + 3)(x - 2) = 0

    So x = 2 or -3.

    -Dan
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  3. #3
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    It says specifiacally to look for any "absolute" extrema though.

    So should I plug both of those numbers back into the original to find where they are maximums and minumums. Should I also plug the 2 numbers in the domain in? If so, how do I know when they are "absolute" extrema?

    If someone could show me how to do this I would be very thankful.
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  4. #4
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    Quote Originally Posted by Mathamateur View Post
    It says specifiacally to look for any "absolute" extrema though.

    So should I plug both of those numbers back into the original to find where they are maximums and minumums. Should I also plug the 2 numbers in the domain in? If so, how do I know when they are "absolute" extrema?

    If someone could show me how to do this I would be very thankful.
    Poor use of language it means find the global extrema in [-2, 4].

    Topsquark has forun the relative extrema of f(x) occur at x=2, -3. Now -3
    is not in the interval so is not what we want.

    Hence the global maximum in [-2,4] occurs at one of the points x=-2, x=2 or x=4, and the global minimum is also at one of these.

    Now f(x) takes values 80, -32, 44 at these points, so the global maximum is 80, and the global minimum is -32.

    RonL
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  5. #5
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    thank you so much, perfectly explained what I was confused on.
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