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Thread: average rate of change - evaluating functions

  1. January 26th 2011, 01:59 PM #1
    epimetheus
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    average rate of change - evaluating functions

    How do you do problems such as this?

    Evaluate \frac{f(x) - f(2)}{x - 2} for f(x) = \frac{4}{x}
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  2. January 26th 2011, 02:28 PM #2
    Aryth
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    Plug and chug:

    \frac{\frac{4}{x} - 2}{x - 2} = \frac{\frac{4 - 2x}{x}}{x-2} = \frac{\frac{2(2 - x)}{x}}{x-2} = \frac{-2}{x}
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  3. January 26th 2011, 02:43 PM #3
    epimetheus
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    Is it the same thing when you have something like \frac{f(3 + h) - f(3)}{h} for x² - 4?
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  4. January 26th 2011, 02:50 PM #4
    Aryth
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    Yes, it's exactly the same:

    \frac{(3 + h)^2 - 4 - (9 - 4)}{h} = \frac{9 + 6h + h^2 - 4 - 9 + 4}{h} = \frac{6h + h^2}{h} = 6 + h
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