Understanding the Average Rate of Change
The average rate of change is a fundamental concept in mathematics and physics that describes how a quantity changes over a specific interval. It's essentially the "average slope" of a function between two points.
For a function $f(x)$, the average rate of change between two points $(x_1, f(x_1))$ and $(x_2, f(x_2))$ is calculated using the formula:
$$ \text{Average Rate of Change} = \frac{f(x_2) – f(x_1)}{x_2 – x_1} $$
This formula represents the total change in the function's output ($f(x)$) divided by the change in its input ($x$). It tells us, on average, how much the function's value increases or decreases for each unit increase in the input variable over that interval.
In physics, this concept is often seen in calculating average velocity (change in position over change in time) or average acceleration (change in velocity over change in time). In economics, it might be used to find the average rate of growth of a company's revenue over a quarter.
How to Use This Calculator:
This calculator allows you to find the average rate of change of a function given two points. You will need to provide the input values ($x_1$, $x_2$) and the corresponding output values ($f(x_1)$, $f(x_2)$) for your function.