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 between the function values at the endpoints of the interval and divide that by the difference between the input values at the endpoints
To find the average rate of change of a function over an interval, we need to calculate the difference between the function values at the endpoints of the interval and divide that by the difference between the input values at the endpoints.
In this case, we are given a table of selected values of the function f. Let’s suppose the table looks like this:
“`
x | f(x)
————
1 | 2
2 | 5
3 | -1
4 | 3
5 | 0
“`
We want to find the average rate of change of f over the interval [1,5]. The function values at the endpoints are f(1) = 2 and f(5) = 0, and the input values at the endpoints are 1 and 5, respectively.
So, the average rate of change can be calculated as follows:
(Change in f) / (Change in x) = (f(5) – f(1)) / (5 – 1) = (0 – 2) / 4 = -2 / 4 = -0.5
Therefore, the average rate of change of f over the interval [1,5] is -0.5.
More Answers:
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Analyzing the Derivative of a Given Function | Finding the True Statement