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 can use the formula:
Average Rate of Change = (Change in output)/(Change in input)
In this case, the interval is [1, 5], which means we need to calculate the change in input and the change in output between the points 1 and 5
To find the average rate of change of a function over an interval, we can use the formula:
Average Rate of Change = (Change in output)/(Change in input)
In this case, the interval is [1, 5], which means we need to calculate the change in input and the change in output between the points 1 and 5.
Given the following table:
x | f(x)
———
1 | 3
2 | 5
3 | 7
4 | 9
5 | 11
To calculate the change in input, we subtract the initial input from the final input:
Change in input = 5 – 1 = 4
To calculate the change in output, we subtract the initial output from the final output:
Change in output = 11 – 3 = 8
Now, we can substitute these values into the formula for average rate of change:
Average Rate of Change = (Change in output)/(Change in input)
= 8/4
= 2
Therefore, the average rate of change of f over the interval [1,5] is 2.
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