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Thread: calculus:average rate of change

  1. #1
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    calculus:average rate of change

    Determine the average rate of change for the following function over the given interval:
    $\displaystyle

    f(x)=x^2
    $ between 3 and 9
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  2. #2
    Senior Member Twig's Avatar
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    hi

    The average rate of change is the following:

    $\displaystyle f(x) \ = \ x^2 $

    We get $\displaystyle f(3) \ = \ 9 $ and $\displaystyle f(9) \ = \ 81 $

    What´s the difference between 81 and 9?
    $\displaystyle 81 - 9 = 72 $

    How many "steps" have we moved on the x-axis? We have moved
    $\displaystyle 9 - 3 = 6 \ \mbox{steps} $

    The average rate of change becomes $\displaystyle \frac{72}{6} \ = 12 $
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  3. #3
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    The average rate of change is the slope of the secant line joining these two points.

    $\displaystyle m_{secant} = \frac{f(9)-f(3)}{9-3} = \frac{81-9}{9-3} = \frac{72}{6} = 12$
    Last edited by Chop Suey; Aug 15th 2008 at 04:07 AM.
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  4. #4
    Senior Member Twig's Avatar
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    hi

    Chop Suey is also definetely correct, except $\displaystyle \frac{72}{6} = 12 \ \mbox{,not 13} $
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