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Math Help - Relative extrema question

  1. #1
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    Relative extrema question

    Find the x-values of all points where the functions defined as follows have any relative extrema. Find the value(s) of any relative extrema.


    f(x)= x^3 + 3x^2 - 24x + 2
    I did f'(x)= 3X^2 + 6X - 24
    0= 3X^2 + 6X - 24 / 3
    0=x^2 +2x-8
    (x+4)(x-2) x=-4 and x= 2
    I did a number line and picked -5, 0, and 3. I plug those numbers to the original problem and -5 came out to be a positive, 0 came out to be a negative, and 3 came out to be a positive.
    f(-4)= (-4)^3 + 3(-4)^2 -24(-4) + 2= . Would -4 be my relative max?
    f(2)= (2)^3 + 3(2)^2 -24(2) +2=-26. Would 2 be my relative min?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by rowdy3 View Post
    Would -4 be my relative max?
    We get relative maximum at x=-4 and the relative maximum is f(-4).

    Same comments for the relative minimum.
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  3. #3
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    rowdy3, I call your attention to the very precise language FernandoRevilla is using. You said (or implied) "the maximum is -4". He is saying the maximum is at x= -4 and the maximum itself is the value of f(-4).
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