college calculus 1

Find the local and absolute extreme values of the function on the given interval. f(x)=x^3-6x^2+9x+1, [2,4]?

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  1. f(x)=x^3-6x^2+9x+1, [2,4]
    f' = 3 x^2 -12 x + 9
    look for zeros in domain
    x^2 -4x + 3 = 0
    (x-3)(x-1) = 0
    x = 1 or x = 3
    3 is in our piece of domain between 2 and 4
    What is function at x = 3 ? Calculate it.

    Then also calculate the function at x = 2 and x = 4

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