Calculating Average Rate of Change in Mathematics: Definition, Formula, and Example

Average Rate of Change

The average rate of change is a concept in mathematics that represents the average rate at which one quantity changes with respect to another quantity over a given interval

The average rate of change is a concept in mathematics that represents the average rate at which one quantity changes with respect to another quantity over a given interval. It measures how quickly or slowly a quantity is changing on average during that interval.

To calculate the average rate of change between two points, you need to determine the difference in the values of the quantity you’re interested in between those two points, and divide it by the difference in the values of the other quantity in the same interval.

Let’s consider an example to better understand how to calculate the average rate of change. Suppose we have a function f(x) = 2x + 1, and we want to find the average rate of change between x = 2 and x = 5.

First, we evaluate the function at x = 2 and x = 5 to find the corresponding values of the function:
f(2) = 2(2) + 1 = 4 + 1 = 5
f(5) = 2(5) + 1 = 10 + 1 = 11

Next, we subtract the initial value (f(2)) from the final value (f(5)):
11 – 5 = 6

Finally, we divide the difference in the function values by the difference in the x-values:
(11 – 5) / (5 – 2) = 6 / 3 = 2

Therefore, the average rate of change of f(x) = 2x + 1 between x = 2 and x = 5 is 2. This means that, on average, the function increases by 2 units for every 1 unit increase in x within that interval.

It is important to note that the concept of average rate of change can be applied to various contexts, such as physics, economics, and other sciences, where quantities are related to each other and change over time or in relation to other variables.

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