Calculating the Average Rate of Change in Math | A Step-by-Step Guide with an Example

Average Rate of Change of f(x) on [a,b]

The average rate of change of a function f(x) on the interval [a,b] refers to the average rate at which the function’s output values change as the input values change from a to b

The average rate of change of a function f(x) on the interval [a,b] refers to the average rate at which the function’s output values change as the input values change from a to b.

To calculate the average rate of change of f(x) on [a,b], you can use the following formula:

Average Rate of Change = (f(b) – f(a))/(b – a)

Here, f(b) represents the value of the function at the upper limit of the interval (b), and f(a) represents the value of the function at the lower limit of the interval (a). (b – a) represents the change in the input values.

Let’s take an example. Suppose we have the function f(x) = 2x + 3, and we want to calculate the average rate of change on the interval [1, 5].

First, we find the value of the function at the upper limit: f(5) = 2(5) + 3 = 13.
Next, we find the value of the function at the lower limit: f(1) = 2(1) + 3 = 5.
Then, we calculate the change in the input values: 5 – 1 = 4.

Finally, we can find the average rate of change:
Average Rate of Change = (f(5) – f(1))/(5 – 1) = (13 – 5)/4 = 8/4 = 2.

Therefore, the average rate of change of f(x) on the interval [1, 5] is 2. This means that the function’s output values, on average, increase by 2 units for every 1 unit increase in the input values within this interval.

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