The average rate of change of a function on the interval [x1, x2] is given by what formula?

The average rate of change of a function \( f(x) \) on the interval \([x_1, x_2]\) is given by the formula:

\[
\frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

This represents the slope of the secant line between the points \((x_1, f(x_1))\) and \((x_2, f(x_2))\) on the graph of the function.

Would you like further details or have any other questions?

Here are 5 related questions you might find interesting:
1. How does the average rate of change differ from the instantaneous rate of change?
2. How do you interpret the average rate of change geometrically?
3. Can the average rate of change be zero on a non-constant function?
4. How does the average rate of change apply to real-world problems like speed?
5. What is the difference between a secant line and a tangent line?

**Tip**: When the interval becomes very small, the average rate of change approaches the derivative, which represents the instantaneous rate of change.

Discover how to calculate the average rate of change of a function using the formula (f(x2) - f(x1)) / (x2 - x1). This concept is key in understanding the slope of the secant line between two points on a graph and is relevant to students in Grades 9-12.

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