1. What is Average Rate of Change?

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

2. How Does the Calculator Work?

The calculator uses the AROC formula:

Where:

• \( f(a) \) — Function value at point a
• \( f(b) \) — Function value at point b
• \( a \) — First point on the x-axis
• \( b \) — Second point on the x-axis

Explanation: The formula calculates the ratio of the change in the function's output to the change in its input between two points.

3. Importance of AROC in Calculus

Details: AROC is fundamental in calculus as it leads to the concept of instantaneous rate of change (derivative) when the interval between points approaches zero.

4. Using the Calculator

Tips: Enter the function values at two points (f(a) and f(b)) and the points themselves (a and b). The points must be different to avoid division by zero.

5. Frequently Asked Questions (FAQ)

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

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

Q3: What units does AROC have?
A: The units are (function output units) per (input units), e.g., m/s for position vs. time.

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

Q5: What does AROC = 0 mean?
A: It means the function has the same value at both points (f(a) = f(b)), indicating no net change.