The Average Rate of Change Formula calculates the slope of a line or a curve on a given range. It is defined as the ratio of the difference in the function f(x) as it changes from 'a' to 'b' to the difference between 'a' and 'b'. The average rate of change is denoted as A(x).

Where,

f(a) and f(x) are the value of the function f(x) at the range 'a' and 'b'.

a and b are the range limit.

Related Calculators | |

Average Rate of Change Calculator | Calculating Rate of Change |

Instantaneous Rate of Change Calculator | Average Calculator |

Some solved problems based on average rate of change are given below:

### Solved Examples

**Question 1: **Calculate the average rate of change of a function, f(x) = 2x + 11 as x changes from 2 to 7 ?

** Solution: **

Given,

f(x) = 2x + 11

a = 2

b = 7

f(2) = 2(2) + 11

f(2) = 4 + 11

f(2) = 15

f(7) = 2(7) + 11

f(7) = 14 + 11

f(7) = 25

The average rate of change is,

A(x) = $\frac{f(b)-f(a)}{b-a}$

A(x) = $\frac{f(7)-f(2)}{7-2}$

A(x) = $\frac{25-15}{5}$

A(x) = $\frac{10}{5}$

A(x) = 2

**Question 2: **A function is given as, f(x) = x^{2} + 2. Calculate the average rate of change of the function if the range of x is (5, 15) ?

** Solution: **

Given,

f(x) = x^{2} + 2

a = 5

b = 15

f(5) = (5)^{2} + 2

f(5) = 25 + 2

f(5) = 27

f(15) = (15)^{2} + 2

f(15) = 225^{} + 2

f(15) = 227

The average rate of change is,

A(x) = $\frac{f(b)-f(a)}{b-a}$

A(x) = $\frac{f(15)-f(5)}{15-5}$

A(x) = $\frac{227-27}{10}$

A(x) = $\frac{200}{10}$

A(x) = 20

Given,

f(x) = 2x + 11

a = 2

b = 7

f(2) = 2(2) + 11

f(2) = 4 + 11

f(2) = 15

f(7) = 2(7) + 11

f(7) = 14 + 11

f(7) = 25

The average rate of change is,

A(x) = $\frac{f(b)-f(a)}{b-a}$

A(x) = $\frac{f(7)-f(2)}{7-2}$

A(x) = $\frac{25-15}{5}$

A(x) = $\frac{10}{5}$

A(x) = 2

Given,

f(x) = x

a = 5

b = 15

f(5) = (5)

f(5) = 25 + 2

f(5) = 27

f(15) = (15)

f(15) = 225

f(15) = 227

The average rate of change is,

A(x) = $\frac{f(b)-f(a)}{b-a}$

A(x) = $\frac{f(15)-f(5)}{15-5}$

A(x) = $\frac{227-27}{10}$

A(x) = $\frac{200}{10}$

A(x) = 20