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 input values (or x-values) at the endpoints
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 input values (or x-values) at the endpoints.
In this question, the interval is [1,5], so the endpoints are x=1 and x=5. We need to find the corresponding function values at these points.
From the table, we can see that at x=1, the function value is f(1) = -3, and at x=5, the function value is f(5) = 11.
Now, we can calculate the difference in the function values: 11 – (-3) = 14.
Next, we calculate the difference in the input values: 5 – 1 = 4.
Finally, we divide the difference in function values by the difference in input values:
Average rate of change = (14) / (4) = 3.5.
Therefore, the average rate of change of f over the interval [1,5] is 3.5.
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