1. What is Average Rate of Change?

The average rate of change represents the slope of the secant line between two points on a function. It measures how much a quantity changes on average between two points.

2. How Does the Calculator Work?

The calculator uses the average rate of change formula:

Where:

• \( (x_1, y_1) \) — First point coordinates
• \( (x_2, y_2) \) — Second point coordinates

Explanation: The formula calculates the ratio of the change in y-values to the change in x-values between two points.

3. Importance of Average Rate of Change

Details: The average rate of change is fundamental in calculus and real-world applications like physics (average velocity), economics (growth rates), and biology (population changes).

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The x-values must be different (x₁ ≠ x₂) to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between average and instantaneous rate of change?
A: Average rate measures change over an interval, while instantaneous rate measures change at a single point (derivative).

Q2: Can the average rate of change be negative?
A: Yes, it's negative when the function is decreasing between the two points.

Q3: What does a zero average rate of change mean?
A: It means there was no net change between the two points (y-values are equal).

Q4: How is this related to slope?
A: The average rate of change is exactly the slope of the line connecting the two points.

Q5: What units does the average rate of change have?
A: The units are the units of y divided by the units of x (e.g., m/s for position vs. time).