Average Rate of Change Formula
The average rate of change function describes the average rate at which one quanity is changing with respect to another. It is a measure of how much the function changed per unit, on average, in that particular interval. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another. Let's look into the Average Rate of Change Formula in detail.
Formula to Calculate Average Rate of Change
The Average Rate of Change function describes the average rate at which one quanity is changing with respect to something another quantity.
The average rate of change formula is given as,
A(x) = [f(b)  f(a)] / (b  a)
where,
A(x) = Average rate of change
f(a) = Value of function f(x) at a
f(b) = Value of function f(x) at b
Let's solve a few practice problems on average rate of change formula.
Solved Examples on Average Rate of Change

Example1: Calculate the average rate of change of a function, f(x) = 2x + 10 as x changes from 3 to 7 using Averafe Rate of change formula.
Solution:
Given:
f(x) = 2x + 10
a = 3
b = 7
f(3) = 2(3) + 10
f(3) = 6 + 10
f(3) = 16
f(7) = 2(7) + 10
f(7) = 14 + 10
f(7) = 24
Using the average rate of change formula,
A(x) = [f(b)−f(a)] / (b−a)
A(x) = [f(7)−f(3)]/ (7−3)
A(x) = (24  16) / 4
A(x) = 8/4
A(x) = 2
Answer: The rate of change is 2 units.

Example 2: Calculate the average rate of change of the function f(x) = x^{2} – 5x in the interval 4 ≤ x ≤ 8.
Solution:
Given: f(x) = x^{2} – 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
Answer: Rate of change A(x) = 7 units.