Selected values of a function f are shown in the table above. What is the average rate of change of f over the interval [1,5] ?
To find the average rate of change of a function over an interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the corresponding input values
To find the average rate of change of a function over an interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the corresponding input values.
In this case, we are given a table with selected values of the function f:
| x | f(x) |
|——-|———|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
We want to find the average rate of change of f over the interval [1, 5]. To do this, we need to calculate the difference in the function values at 5 and 1, divided by the difference in the corresponding input values (5 – 1).
f(5) – f(1) = 10 – 2 = 8
5 – 1 = 4
Therefore, the average rate of change of f over the interval [1, 5] is 8/4 = 2.
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