math - very urgent !

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Verify that f(x) = x^3 − 2x + 6 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3]
and find all values of C that satisfy the conclusion of the theorem.

  • math - very urgent ! -

    f' = 3 x^2 -2

    at -2 f(-2) = -8+4+6 = 2
    at 3 f(3) = 27-6+6 = 27

    mean slope = (27-2)/5 = 5
    is f' = 5 in between -2 and +3?

    5 = 3 x^2-2
    3 x^2 = 7
    x^2 = 7/3
    x = - 1.53 and +1.53
    both are between x = -2 and x = +3

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