1. What is Average Rate of Change?

The Average Rate of Change (AROC) between two points measures how much a quantity changes on average between those points. In mathematics, it represents the slope of the secant line between two points on a curve.

2. How Does the Calculator Work?

The calculator uses the AROC formula:

Where:

• \( y2 \) — y-coordinate of the second point
• \( y1 \) — y-coordinate of the first point
• \( x2 \) — x-coordinate of the second point
• \( x1 \) — x-coordinate of the first point

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

3. Importance of AROC Calculation

Details: Average rate of change is fundamental in calculus and real-world applications. It's used to determine velocity, growth rates, and other change-related measurements.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between AROC and instantaneous rate of change?
A: AROC measures change between two points, while instantaneous rate of change (derivative) measures change at a single point.

Q2: Can AROC be negative?
A: Yes, AROC is negative when the function is decreasing between the two points.

Q3: What does AROC = 0 mean?
A: It means there's no change in the y-values between the two points (the function is constant).

Q4: What units does AROC have?
A: The units are (y-units) per (x-units), depending on your quantities (e.g., m/s, $/month).

Q5: How is AROC related to slope?
A: AROC is exactly the slope of the straight line connecting the two points on the graph.