# Rate of Change

Consider the function **y = f(x)** and consider two points on the x-axis "**a**" and "**a + h**", with "**h**" being a real number that corresponds to the increase of x (**Δx**).

The **rate of change** of a function on the interval **[a, a + h]**, denoted by **Δy** is the **difference between the ordinates** corresponding to points on the x-axis, **a** and **a + h**.

**Δy = [f(a+h) − f(a)]**

## Average Rate of Change

**Average rate of change** in the interval **[a, a + h]** is represented by or , and is the quotient between rate of change and the amplitude of the interval considered on the horizontal axis, **h** or **Δx.** It can be written as follows:

### Geometric Interpretation

The previous expression coincides with the slope of the **secant line to the function f(x)**, that passes through the points **P** and **Q** (represented on the graph above) which are represented on the x-axis as **a** and **a + h**.

In the triangle **PQR**, we can see that:

#### Examples

Calculate the average rate of change of the function f(x) = x^{2 } − x in the interval [1,4].

A stock market index increased from 1,350 to 1,510 points in one year. Find the average monthly rate of change.