Average Rate of Change
The average rate of change refers to the average rate at which a quantity changes over a specific interval of time or a particular range of values
The average rate of change refers to the average rate at which a quantity changes over a specific interval of time or a particular range of values. In mathematics, it is often used to describe the rate of change of a function over an interval on a coordinate plane.
To calculate the average rate of change of a function, you need to find the difference in the values of the function between two points on the interval and divide it by the difference in the corresponding inputs (or independent variable values). This gives you the slope of the line connecting the two points, which represents the average rate of change.
The formula for the average rate of change of a function f(x) over the interval [a, b] is:
Average Rate of Change = (f(b) – f(a)) / (b – a)
For example, let’s consider a linear function f(x) = 3x + 2. To find the average rate of change of the function between x = 1 and x = 3, we need to plug these values into the formula:
Average Rate of Change = (f(3) – f(1)) / (3 – 1)
= (3(3) + 2) – (3(1) + 2)) / (3 – 1)
= (9 + 2) – (3 + 2)) / 2
= (11 – 5) / 2
= 6 / 2
= 3
Hence, the average rate of change of this linear function over the interval [1, 3] is 3. This means that, on average, the function increases by 3 units for every increase of 1 unit in the input value within this interval.
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