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Math Help - Rate of change?

  1. #1
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    Question Rate of change?

    Whats the average rate of change between x=6 and x=-6 for
    f(x)=8x^2+1x+10
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  2. #2
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    Hello, sadieann!

    Are you waiting for a formula?


    Find the average rate of change between x=\text{-}6 and x=6 for f(x)\:=\:8x^2+1x+10

    \begin{array}{cccccc}\text{When }x=\text{-}6\!: &f(\text{-}6) &=& 8(\text{-}6)^2 + (\text{-}6) + 10 &=& 292 \\<br />
\text{When }x = 6\!: & f(6) &=& 8(6^2) + 6 + 10 &=& 304\end{array}

    The function changed by: f(6) - f(\text{-}6) \:=\:304 - 292 \:=\:+12 units
    . . over a distance of: 6 - (\text{-}6) \:=\:12 units.

    Therefore, the average rate of change is: . \frac{12}{12} \:=\:1

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  3. #3
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    if you are still waiting ...

    the average rate of change for the function f over the interval [a,b] is

    \frac{f(b) - f(a)}{b-a}
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