Average Rate of Change Formula
The Average Rate Of Change Formula describes the rate at which one quantity changes in relation to another. The average Rate Of Change Formula indicates how much the function changed per unit during the specified interval. When calculating the rate of change in one item, the amount of change in one is divided by the corresponding amount of change in another.
After reading about the formula, many students have the question in mind: Which formula is used to find the rate of change of a linear function? Students need to earn this for a linear function, the rate of change for a linear function is shown in a table or on a graph as the parameter (m) in the slope-intercept form for a line: y=mx+b.
Formula for the Average Rate of Change of a Function
Students will read about the formula for the ratio of change in one quantity to change in another. It measures the function’s change in value per unit over a specific period. If f(x) is a function and [a, b] is an interval, then A(x) = [f(b) – f(a)] / (b – a)
Solved Examples
One example of the Average Rate Of Change Formula is given below:
Evaluate the average rate of change of the function f(x) = x2 – 5x in the interval 4 ≤ x ≤ 8.
Solution:
Given: f(x) = x2 – 5x, a = 4, b = 8.
- f(4) = f(4) = (4)2 – 5(4) = 16 – 20 = -4
- f(8) = f(8) = (8)2 – 5(8) = 64 – 40 = 24
Using the average rate of change formula,
A(x) = [f(b)−f(a)] / (b−a)
= (24−(−4)) / (8−4)
= 28/4
= 7
Therefore, rate of change A(x) = 7.
Students can access information about the Average Rate Of Change Formula from the Extramarks website or mobile application.