1. What is Average Rate of Change?

The Average Rate of Change (ARC) measures how much a quantity changes on average between two points. In mathematics, it represents the slope of the secant line between two points on a function's graph.

2. How Does the Calculator Work?

The calculator uses the Average Rate of Change formula:

Where:

• \( f(a) \) — Function value at point a
• \( f(b) \) — Function value at point b
• \( a \) — First point
• \( b \) — Second point

Explanation: The formula calculates the ratio of the change in function values to the change in input values between two points.

3. Importance of Average Rate of Change

Details: Average Rate of Change is fundamental in calculus and real-world applications. It helps understand how quickly a quantity is changing over an interval, with applications in physics (velocity), economics (marginal cost), and many other fields.

4. Using the Calculator

Tips: Enter the function values f(a) and f(b), and the corresponding points a and b. Ensure that a and b are different values to avoid division by zero.

5. Frequently Asked Questions (FAQ)

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

Q2: Can average rate of change be negative?
A: Yes, a negative ARC indicates the function is decreasing over the interval.

Q3: What does a zero average rate of change mean?
A: A zero ARC means the function values at both points are equal, indicating no net change over the interval.

Q4: How is average rate of change related to slope?
A: The ARC equals the slope of the secant line connecting the two points on the function's graph.

Q5: Can I use this for non-linear functions?
A: Yes, the average rate of change formula works for any function, linear or non-linear.