The table of values represents a polynomial function f(x). How much greater is the average rate of change over the interval [5, 7] than the interval [2, 4] ?

x f(x)
2 230
3 638
4 1048
5 3452
6 4568
7 5002
8 6294
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Given:

The table of values of the function f(x).

To find:

How much greater is the average rate of change over the interval [5, 7] than the interval [2, 4]?

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

The average rate of change over the interval [5, 7] is:

The average rate of change over the interval [2,4] is:

The difference between the average rate of change over the interval [5, 7] and the interval [2, 4] is:

Therefore, the average rate of change over the interval [5, 7] is 366 more than the interval [2, 4].

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