# How to find average rate of change of a function?

Assuming you mean the average rate of change of a function over an interval, the easiest way to do this is to take the derivative of the function and then evaluate the derivative at the midpoint of the interval. Now I will tell you **How to find average rate of change of a function?** Keep reading to know more.

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## Way to find average rate of change of a function?

The average rate of change of a function is the ratio of the change in the dependent variable to the change in the independent variable.

To find the average rate of change of a function, take two points on the function and find the slope of the line between those points. This will give you the average rate of change between those two points.

And to find the average rate of change of a function over a specific interval, take the derivative of the function and evaluate it at the endpoints of the interval. This will give you the average rate of change of the function over that interval.

**Example: Find the average rate of change of the function**

f(x)=x2+3x+4

over the interval [1,4].

f ‘(x) = 2x + 3

f ‘(1) = 2(1) + 3 = 5

When **f ‘(4) = 2(4) + 3 = 11**

**Average rate of change = (11 – 5)/(4 – 1) = 6/3 = 2**

## What is the formula to find the average rate of change?

The average rate of change is found by dividing the change in y by the change in x.

For example, if the y-values of a function increase by 3 when the x-values increase by 2, then the average rate of change is 3/2.

The average rate of change can also be found by taking the derivative of a function at a specific point.

For example, if the derivative of a function at x=2 is 6, then the average rate of change is 6.

## How do I find the average rate of change of a function when given a function and two inputs?

To find the average rate of change of a function when given a function and two inputs, one would take the difference in the outputs of the function at the two inputs and divide it by the difference in the inputs.

For example, if we were given the function f(x) = x^2 and the inputs a = 2 and b = 4, we would take f(4) – f(2) = 16 – 4 = 12 and divide by 4 – 2 = 2 to get an average rate of change of 6.

We could also take the derivative of the function at a specific point within the two inputs – say, at x = 3 – and use that as our average rate of change. In this case, we would have f'(3) = 6x = 18.

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

Yes, an average rate of change is the same as the slope. The slope is defined as the change in y over the change in x, and the average rate of change is defined as the change in y over the change in x. So, they are equivalent.

The average rate of change is a measure of how a function is changing. It is the average rate at which the function is increasing or decreasing. It is important because it can help us predict how a function will change in the future.