1. What is Average Rate Of Change?

The Average Rate Of Change (ARC) of a function between two points is the change in the function's value divided by the change in the input value. It represents the slope of the secant line between these two points on the graph of the function.

2. How Does the Calculator Work?

The calculator uses the ARC formula:

Where:

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

Explanation: The formula calculates the slope of the straight line connecting two points on a function's graph, representing the average rate at which the function changes between these points.

3. Importance of Average Rate Of Change

Details: ARC is fundamental in calculus and real-world applications. It helps understand how quantities change relative to each other, appearing in physics (velocity), economics (marginal cost), and many other fields.

4. Using the Calculator

Tips: Enter the function values at points a and b (f(a) and f(b)), and the points themselves (a and b). Points a and b must be different (b ≠ a).

5. Frequently Asked Questions (FAQ)

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

Q2: What does a negative ARC indicate?
A: A negative ARC means the function is decreasing on average between the two points.

Q3: Can ARC be zero?
A: Yes, when f(a) = f(b), indicating no net change between the points.

Q4: How is ARC related to slope?
A: ARC is exactly the slope of the secant line connecting the two points on the function's graph.

Q5: What are common applications of ARC?
A: Applications include calculating average velocity, growth rates in biology, and marginal analysis in economics.