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Math Help - question about mean value

  1. #1
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    question about mean value

    f(x) = x^3 - 5x^2 - 3x
    find the mean value theorem to find all numbers c in the interval (1,3)

    i got the answer 5 +- (sqrt 16) / 3
    am i correct
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  2. #2
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    Quote Originally Posted by dangerous1 View Post
    f(x) = x^3 - 5x^2 - 3x
    find the mean value theorem to find all numbers c in the interval (1,3)

    i got the answer 5 +- (sqrt 16) / 3
    am i correct

    What is "all numbers c in the interval (1,3)"??
    And no, you cannot be correct, whatever c is, since both numbers 5\pm \frac{\sqrt{16}}{3}=5\pm \frac{4}{3} are not in (1,3)...even if the numbers were \frac{5\pm 4}{3} they still aren't in the interval (1,3).

    Tonio
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  3. #3
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    Quote Originally Posted by dangerous1 View Post
    f(x) = x^3 - 5x^2 - 3x
    find the mean value theorem to find all numbers c in the interval (1,3)

    i got the answer 5 +- (sqrt 16) / 3
    am i correct
    \frac{f(3) - f(1)}{3-1} = -10

    f'(x) = 3x^2 - 10x - 3 = -10

    3x^2 - 10x + 7 = 0

    factor and finish solving for x.
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