Mathematics

Question

F(x)= x^3-9x
What is the average rate of change of f over the interval [1,6]?

2 Answer

  • Answer: 34

    Step-by-step explanation:

  • The average rate of change of f(x)= x³-9x in interval [1,6] is 34.

    Average rate of change

    If f(x) is a function the [a,b] is interval then the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

    How to find the average rate of change of f?

    Given the function is f(x)= x³-9x and the interval is [1,6].

    then first we have to find the value of f(1) and f(6).

    So  

    f(1) = (1)³-9(1)

        = 1-9

        = -8

    and

    f(6) = (6)³-9(6)

        = 216- 54

        = 162

    therefore average rate of change of f is

    [tex]\frac{f(6)-f(1)}{6-1}= \frac{162+8}{6-1}[/tex]

                  = 170/5

                  = 34

    Hence the average rate of change of f is 34.

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