The Average Rate of Change calculator is used to find the average rate of a function over the specified interval. It's a rate that indicates how one number typically changes with another. The average rate of change is displayed in a matter of seconds using The Mathematics Master online average rate of change calculator.

\( A = \dfrac{f(x_2) – f(x_1)}{x_2 – x_1} \)

It generally describes how one quantity varies as the other value changes. In other words, the total change in the output function divided by the change in input values is the average rate of change of a given function between input values.

The average rate of change formula is:

\( A = \dfrac{f(x_₂) – f(x_₁)}{x_₂ – x_₁} \)

The average rate of change is equal to the sum of the function’s output changes divided by the input changes.

Before finding the rate of change, we need to define the function we’ll use to determine, together with an interval [a, b].

The average rate of change can then be calculated using the slope formula. The average rate of change is essentially a slope, but one that uses a function rather than a linear slope that brings the average between two points to zero.

Using the following steps, this online calculator calculates the average rate of change:

- First, enter a function for determining the average rate in the input field, such as f(a), f(b), a value, and b value.
- Select “Calculate Average Rate of Change.”
- Finally, the calculator will show the average rate of change.

What is the rate of change?

The rate of change describes the relationship between two quantities. It can be positive or negative. For example, we know that a line’s slope is the ratio of the vertical and horizontal change between two points on a plane or a line, therefore the slope is the ratio of rise to run.

Where,

Rise is the difference in height between any two places.

Run is the difference in direction between two places.

**Hence, the Rate of Change Formula**

The rate of change is:

Rate of change \( = \dfrac{Rise}{Run} \) \( = \dfrac{Δy}{Δx} \)

Is the slope the same as the average rate of change?

A function’s average rate of change shows how it alters between two points. In contrast, we define a function’s slope as the slope of the line tangent to the curve at a particular point. Every point changes the same way in a linear function, so the average rate of change and slope are both equal.

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