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Calculus

Find the local maximum and local minimum of the function. f(x) = x^3 − 12x^2 − 27x + 7

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  1. dy/dx = 3x^2 - 24x - 27
    = 0 for a max/min

    divide by 3
    x^2 - 8x - 9 = 0
    it factors nicely ...
    (x-9)(x+1) = 0
    x = 9 or x = -1

    f(9) = .....
    f(-1) = ....

    take over.

    this confirms our work
    http://www.wolframalpha.com/input/?i=plot+f%28x%29+%3D+x%5E3+%E2%88%92+12x%5E2+%E2%88%92+27x+%2B+7

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  2. Those are the answers I got that I thought were wrong, but the online assignment wanted the value of f(9)=-479 and f(-1)=21, not 9 and -1. Thank you!

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  3. exactly.

    I left it up to you to finish the problem.
    Oh well ....

    f(9) = 9^3 - 12(9)^2 - 27(9) + 7
    = -479

    etc for f(-1) = 21

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  4. btw, I also did your other very long question.
    Did you look at it ?

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