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# Average Rate of Change Calculator

Enter the function & write the interval value in the given input box and press the “**Calculate**” button to find the average rate of change using the Average Rate of Change calculator.

The Average Rate of Change calculator is a useful tool that helps to find the average rate of change for a given function over a specified interval. This calculator performs the calculations faster and determines the average rate of change in seconds.

**What is The Average Rate of Change?**

The Average Rate of Change is a number that is either positive or negative and also plays an important role in calculus. The average rate of change of a function over an interval provides a measure of how the function’s value changes on average between two points or interval values. It represents the slope of the line connecting these two points on the function’s graph.

**Average Rate of Change Formula**

The average rate of change of a function f(x) from “`x=a to x=b`

” is find by the below formula:

Average Rate of Change = `f(b)−f(a) / b-a`

Where

- f(a) shows the value of the function at the starting point “
**a”**. - f(b) is the value of the function at the ending point “
**b”**. **b−a**is the length of the interval.

**How to Find Average Rate of Change?**

Here we solved the manual example to evaluate the average rate of change on a specific interval.

**Example**

Calculate the Average rate of change of a function, `f(x) = 3x + 5`

as “x” changes from 5 to 9.

**Solution**

**Step 1:** Write the data from the above given statement.

f (x) = 3x+5, a = 5, b = 9

**Step 2:** Put the interval values in the given function.

f (5) = 3(5) + 5 = 20

f (9) = 3 (9) + 5 = 32

Put values in the average rate of change formula,

Average Rate of Change = 32-20/ 4

= 12/4

= 3

**Why Choose Our Average Rate of Change Calculator?**

The reasons for choosing the average rate of change calculator are not specific but here they have some common reasons.**User-Friendly Interface**

Our Calculator is designed with a simple and friendly interface that is easy to use for everyone. You can easily put data and get the output or result without any difficulty.

**Step-by-Step Solutions**

One of the standout features of our calculator, it provides detailed steps with complete explanations without any fee. This helps the user to understand the concept of the average rate of change more easily.

**Versatile**

Our average rate of change calculator finds the rate of change of different complex functions such as: Trigonometric function, Sin function, Cosine function, etc,.

**Frequently Asked Questions (FAQs)**

**What is the average rate of change often called?**

The average rate of change is often called the slope.

Average Rate of Change = Slope

**Can the average rate of change be negative?**

Yes, the value of the average rate of change can be negative because it represents the slope of the graph. Thus, if the slope of the graph is negative then the average rate of change is negative.

**What is the symbol for the average rate of change?**

The symbol used for average rate of change is shown as “**∆**” which is taken from Greek or read as “**delta**”. It is commonly used as an abbreviation for **“change in”** something. For example: ∆y read as** “change in y”**.

### References

- What is Average rate of change? | Khan Academy
- How to find Average rate of change? | Calcworkshop