1. What is Rate of Change?

The rate of change (ROC) measures how one quantity changes in relation to another. In mathematics, it represents the ratio of the change in the output value to the change in the input value.

2. How Does the Calculator Work?

The calculator uses the Mathway method formula:

Where:

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

Explanation: This formula calculates the average rate of change between two points on a function, which is equivalent to the slope of the secant line between these points.

3. Importance of Rate of Change

Details: Rate of change is fundamental in calculus and real-world applications like physics (velocity), economics (marginal cost), and biology (growth rates). It's the precursor concept to derivatives.

4. Using the Calculator

Tips: Enter the function values at points a and b, and the corresponding a and b values. Ensure (b - a) is not zero to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between average and instantaneous rate of change?
A: Average ROC measures change over an interval, while instantaneous ROC (derivative) measures change at a single point.

Q2: What units does ROC have?
A: The units are (output units) per (input units), like meters/second or dollars/year.

Q3: Can ROC be negative?
A: Yes, negative ROC indicates the output decreases as the input increases.

Q4: How is this related to slope?
A: For linear functions, ROC is constant and equals the slope. For non-linear functions, it's the slope of the secant line between two points.

Q5: What if b = a?
A: The calculation is undefined (division by zero) as there's no interval to measure change over.