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, you need to determine the difference in the function’s values at the endpoints of the interval and divide it by the difference in the input values (also known as the independent variable) at the endpoints of the interval
To find the average rate of change of a function over an interval, you need to determine the difference in the function’s values at the endpoints of the interval and divide it by the difference in the input values (also known as the independent variable) at the endpoints of the interval.
In this case, the given interval is [1,5]. To calculate the average rate of change of f over this interval, we will use the formula:
Average Rate of Change = (f(5) – f(1)) / (5 – 1)
Looking at the table provided, we see that f(1) = 3 and f(5) = 15. Plugging these values into the formula, we get:
Average Rate of Change = (15 – 3) / (5 – 1)
= 12 / 4
= 3
Therefore, the average rate of change of f over the interval [1,5] is 3.
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