The average rate of change of any function gives the average rate at which one function varies with respect to the other. In simple words it calculates slope $\frac{dy}{dx}$ from point a to b. The average rate of change is given by

Where f(a) and f(b) are given two functions. Here A(x) is the average rate of change, f(b) - f(a) gives the change in the function as the input varies from point a to b. (b - a) gives the change in function f.

Average rate of change Calculator is a online tool that calculates the average rate of change of any given function. It calculates the slope of any two given functions. Provided are the blocks for f(a), f(b), b and a values where you are supposed to enter the values to get the answer instantly.

## Average Rate of Change Examples

Steps to find the average rate of change

Step 1: Read the given problem, note down the values a,b and calculate the given functions f(a) and f(b).

Step 2 : Use Average rate of change formula
A(x) = $\frac{f(b) - f(a)}{b - a}$
Substitute the values, Simplify and get the answer.

Below are given some solved problems based on average rate of change which may be helpful for you.

### Solved Examples

Question 1: Find the slope of the curve f(x) = $\frac{5x^{2}}{2}$ as x changes from 4 to 1?
Solution:

Step 1 : Given: a = 1 and b = 4
f(1) = $\frac{5 (1)^{2}}{2}$ = 2.5

f(4) = $\frac{5 (4)^{2}}{2}$ = 40

Step 2 : Using Average rate of change formula we have
A(x) = $\frac{f(4) - f(1)}{4 - 1}$

= $\frac{40 - 2.5}{4 - 1}$

= 12.5.
The average rate of change is 12.5.

Question 2: Find the average rate of change of the function f(x) = x + 5 as x changes from 3 to -1?
Solution:

Step 1 : Given: a = 1 and b = 4
f(-1) = -1 + 5 = 4
f(3) = 3 + 5 = 8

Step 2 : Using Average rate of change formula we have
A(x) = $\frac{f(4) - f(1)}{4 - 1}$

= $\frac{8 - 4}{3 - (-1)}$

= 1.
The average rate of change is 1.

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