1. What is Average Rate of Change?

The average rate of change represents how much one quantity changes, on average, relative to another. In mathematics, it's the slope of the secant line between two points on a function.

2. How Does the Calculator Work?

The calculator uses the average rate of change formula:

Where:

• \( y_2 \) — Final y-value
• \( y_1 \) — Initial y-value
• \( x_2 \) — Final x-value
• \( x_1 \) — Initial x-value

Explanation: The formula calculates the ratio of the change in the dependent variable (y) to the change in the independent variable (x) between two points.

3. Importance of Average Rate of Change

Details: Average rate of change is fundamental in calculus, physics, economics, and other sciences. It helps understand trends, velocities, growth rates, and other dynamic relationships between variables.

4. Using the Calculator

Tips: Enter the y and x values for two points. The calculator will compute the average rate of change between these points. Ensure x₂ ≠ x₁ to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: How is average rate different from instantaneous rate?
A: Average rate measures change over an interval, while instantaneous rate measures change at a single point (derivative).

Q2: What does a negative average rate indicate?
A: A negative rate means the y-value decreases as the x-value increases (negative slope).

Q3: Can this be used for non-linear functions?
A: Yes, but it only gives the average slope between two specific points, not the overall behavior.

Q4: What units does the result have?
A: The units are (y-units)/(x-units), like m/s for position vs. time.

Q5: How is this related to slope?
A: The average rate of change is exactly the slope of the line connecting two points on a graph.