Calculating the Average Rate of Change in Mathematics | Understanding the Concept and Formula

Average Rate of Change

The average rate of change, also known as the average rate of variation, is a concept in mathematics that measures the rate at which a quantity changes over a specific interval

The average rate of change, also known as the average rate of variation, is a concept in mathematics that measures the rate at which a quantity changes over a specific interval. It is a way to determine the average rate at which one variable is changing with respect to another variable.

To calculate the average rate of change, you need to determine the difference in the values of the variable you are interested in over the given interval. You then divide this difference by the change in the other variable over the same interval.

Mathematically, the average rate of change is given by the formula:

Average Rate of Change = (Change in y)/(Change in x),

where “Change in y” represents the difference in the values of the dependent variable (y) and “Change in x” represents the difference in the values of the independent variable (x) over the interval.

For example, consider the function f(x) = 2x + 3. Let’s calculate the average rate of change of f(x) between x = 1 and x = 5.

First, we determine the change in y. Substituting x = 5 into the function, we get f(5) = 2(5) + 3 = 13. Substituting x = 1 into the function, we get f(1) = 2(1) + 3 = 5. The change in y is 13 – 5 = 8.

Next, we determine the change in x. The change in x is 5 – 1 = 4.

Now we can calculate the average rate of change using the formula: Average Rate of Change = (Change in y)/(Change in x) = 8/4 = 2.

Hence, the average rate of change of f(x) between x = 1 and x = 5 is 2. This means that, on average, the function f(x) is increasing by 2 units for every 1 unit increase in x over this interval.

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