1. What is Rate of Change?

The rate of change (ROC) measures how much a quantity changes with respect to another quantity. 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 rate of change formula:

Where:

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

Explanation: The formula calculates the average rate of change between two points on a function. This 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, physics, economics, and many other fields. It's used to analyze trends, velocities, growth rates, and more.

4. Using the Calculator

Tips: Enter the function values at points a and b, and the corresponding input values. The points must be distinct (b ≠ a) 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: Can rate of change be negative?
A: Yes, a negative ROC indicates the function is decreasing over the interval.

Q3: What units does ROC have?
A: The units are output units per input unit (e.g., meters per second for position vs. time).

Q4: How is ROC 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.

Q5: What does a ROC of zero mean?
A: It means there's no change in the output between the two input values (constant function over that interval).