For a function g(x), the difference quotient is StartFraction 6 Superscript x + h minus 3 Baseline minus 6 Superscript x + 3 Baseline Over h

Question

For a function g(x), the difference quotient is StartFraction 6 Superscript x + h minus 3 Baseline minus 6 Superscript x + 3 Baseline Over h EndFraction. What is the average rate of change of g(x) on the interval from x = –2 to x = 1?

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RobertKer 5 months 2021-08-30T09:35:47+00:00 1 Answers 0 views 0

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    2021-08-30T09:37:32+00:00

    Answer:

    The average rate of change in that interval is 1.99

    Step-by-step explanation:

    Here we have that the difference quotient for g(x) is:

    \frac{6^{x + h} - 3 - 6^x + 3}{h}

    Remember that for a general function f(x), the difference quotient is:

    \frac{f(x + h) - f(x)}{h}

    So if we look at the difference quotient for g(x), we can conclude that:

    g(x) = 6^x - 3

    Also remember that the average rate of change in an interval (a, b) is just:

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

    So here we want the average rate of change of g(x) in the interval from x = -2 to x = 1, this is:

    R = \frac{(6^1 - 3) - (6^{-2} - 3)}{1 - (-2)}  = \frac{6 - 6^{-2}}{3} = 1.99

    The average rate of change in that interval is 1.99

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