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Math Help - Slope Help?

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    24

    Slope Help?

    f(x)-------x
    31.25-----2.5
    39.20-----2.8
    45--------3.0
    48.05-----3.1

    The function f is differentiable and has values as shown in the table above. Both f and f ' are strictly increasing on the interval [0,5]. Which of the following could be the value of f ' (3)?

    a. 20
    b. 27.5
    c. 29
    d. 30
    e. 30.5

    I've already ruled out choice a and b, but between c, d, and e, I don't know which one is correct.
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  2. #2
    Newbie Mirado's Avatar
    Joined
    Apr 2009
    From
    New York
    Posts
    18

    solved.... maybe

    When I did a quadratic regression, and derived the formula, I got:  4.79\bar{54} x + 1.106\bar{81}

    so, once you put in 3, you get roughly  29.879\bar{54}

    So, I'd say it's D.

    But to have a more clear answer, if you take the slope between points (3,45) and (2.8,39.2); you get 29.
    Then with points (3.1,48.05) and (3,45); you get 30.5

    Obviously then since the function is continuous, it must be in between 29 and 30.5, which gives option D.

    hope this helps.
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