## What is the Average Rate of Change Calculator?

The average rate of change calculator is an online tool that helps you **find the rate of change** of a function. It is used to simplify the process of finding change in quantities over time under certain conditions.

Our average rate of change formula calculator is a versatile tool that can easily do complex calculations of change of an object or quantity over a period. It is the best learning source for students, teachers, and professionals, as it provides information about different objects' average rate of change.

## What is the Average Rate of Change?

An average rate of change of a function is a process in which the **change in a quantity** is divided by its input value over a closed interval in calculus. It provides information about the change in given quantity per unit of change over a specific condition that affects on it.

This method is used in many scientific fields to observe the rate of change in the original quantity; in physics, it is used to find the rate of change in velocity. On the other hand in biology, it is used to find the growth and decay rate, etc.

## What is the Average Rate of Change Formula?

The average rate of change expresses the slope of a line that passes through the points (a, f(a)) and (b, f(b)) on the graph of the function. It provides a rate of a function f(x) that changes per unit change in x under the given interval as [a, b]. Mathematically, the average rate of change **formula** is:

$$ Average\;Rate\;of\;Change \;=\; \frac{Change\;of\;Output}{Change\;of\;input} \;=\; \frac{f(b) - f(a)}{b - a} $$

Where:

- f (a) and f (b) are the points a and b of the function, respectively.
- a and b are the points over an interval.

## How to Find the Average Rate of Change?

We use its formula to calculate average rate of change, which makes our calculations easier and simpler, especially when manually evaluating the given function. Now let us explain the calculation of average rate of change in steps.

- First,
**determine the given values**as f(x) and the interval value [x1, x2], in which the first value denotes “a” and the second value is “b.”

- Then, add the values of a and b in the given function f(x) to find the values of f(a) and f(b).

- After that, find the difference between a and b as b-a.

- Put the values of f(a), f(b), and b-a in the average rate formula and simplify it.

- After simplification, you get a solution for the average rate of change in the given function.

You can also use our average rate of change over an interval calculator, which offers precise results along with step-by-step instructions in just a few seconds, to calculate average rate of change.

## Solved Example of Average Rate of Change:

Let's see an **example** with the solution of the average rate of change to get better clarity about this concept.

**Example:**

Calculate the average rate of change of f(x) = x^{2} - 1/x on the interval [2,4].

**Solution:**

Identify the interval and put its values in the given function f(x) to find the values of f(a) and f(b).

$$ f(2) \;=\; 2^2 - \frac{1}{2} \;=\; 4 - \frac{1}{2} \;=\; \frac{7}{2} $$

$$ f(4) \;=\; 4^2 - \frac{1}{4} \;=\; 16 - \frac{1}{4} \;=\; \frac{63}{4} $$

Apply the average rate formula:

$$ Average\;Rate\;of\;Change \;=\; \frac{f(b) - f(a)}{b - a} $$

Put the values of a, b, f(a), and f(b) in the above formula. Then simplify it to the solution of the average rate of change of the given function.

$$ Average\;rate\;of\;change \;=\; \frac{f(4) - f(2)}{4 - 2} \;=\; \frac{\frac{63}{4} - \frac{7}{2}}{4 - 2} $$

$$ =\; \frac{\frac{49}{4}}{2} \;=\; \frac{49}{8} $$

## How to Use the Average Value of a Function Calculator?

The average rate of change calculator has a simple design, so everyone can use it to calculate the function average rate on the given x-value points. Before adding the input value, you must follow some instructions. These instructions are:

- Enter the value of the given function f(x) in the input box.
- Enter the value of the closed interval in the form of a and b in the next input box.
- Review your input value before hitting the calculate button to start the calculation process to find the solution to the function average rate.
- Click on the “
**Calculate**” button to get the required result for the average rate of change problem. - If you want to try out our average rate of change over an interval calculator for the first time, then you can use the load example.
- Click on the “Recalculate” button to get a new page for solving more average rate of change over an interval [a, b].

## Output from Average Rate Change Calculator:

The avg rate of change calculator gives you the solution to a given function problem when you input the value into it. It may be included as:

**Result Option**:

You can click on the result option, and it will provide you with a **solution for the rate of change** of function questions.

**Possible Step**:

The Possible Steps option provides you with a solution in which evaluation steps for an average rate of change over closed interval questions.

## Benefits of Using Average Rate of Change Formula Calculator:

The average value of a function calculator has many **valuable benefits** that help you get the solution of the average rate of change function whenever you use it. These benefits are:

- It saves your time and effort from doing lengthy and complex calculations of the average rate of change question in less than a minute.
- Our average rate change calculator is a free tool that you can use to find the average rate of change for a question without paying any charge.
- The average rate of change calculator is an easy-to-use tool, so you do not need any technical expertise. Just use it to calculate the given function average rate problems easily.
- It is a reliable tool that provides you with accurate solutions every time whenever you use it to calculate the average rate for function problems.
- The avg rate of change calculator provides you with a solution procedure in a step-by-step method for more clarity.