# Average Rate of Change Calculator

Enter the function f(x), X₁ and X₂ values in the average rate of change calculator to know the f(x₁), f(x₂), f(x₁)-(x₂), (x₁-x₂), and the rate of change.

Use this online average rate of change calculator that helps you to determine the average rate of a function on the given interval. Well, it is a rate that tells how a number changes on average with another. So, let’s dive in, to understand how to find average rate of change with a formula.

## What is the Average Rate of Change?

Generally, it defines how one quantity changes with the change in the other value. In other words, the average rate of change of a given function between input values is expressed as the total change of the output function divided by the change in input values.

### Average Rate of Change Formula:

The standard average rate of change equation is: $$\frac {f(b)−f(a)} {b−a}$$ Where, • (a, f(a)) are coordinates of the first point • (b, f(b))are coordinates of other point.

## How to Find Average Rate of Change of a Function?

If you know the intervals and a function, then, we apply the standard formula that calculates the average rate. Example: Find the average rate of change of function f(y) = 3y2 + 5 on the y interval (-1, 3). Solution: Where value of set a = -1 and b = 3 so that “a” is the left interval, and b is the right side on interval. $$f(a) = 3(-12) + 5 = 8$$ $$f(b) = 3(32) + 5 = 32$$ Now, let’s substitute values into the average rate of change formula. $$\frac{(32 – 8)}{(3 – (-1))}$$ $$\frac{24}{4} = 6$$

## How Average Rate of Change Calculator Works?

### Input:

• Firstly, enter a function for calculating the average rate. • Now, plug in the values of the interval • Press the calculate button

### Output:

• Initially, the calculator displays the given function and interval. • Then, provide the stepwise solution. • Hence, you can do calculations numerous times by click on the “Recalculate” button.

## Reference:

From the source of Wikipedia: Slope Formula, Calculating Slope from a Graph, Slope Formula and Coordinates, Slope of Horizontal and Vertical Lines. From the source of Brilliant: Average and Instantaneous Rate of Change, Instantaneous Rate of Change.