1. What is Rate of Change?

The rate of change (ROC) measures how much a quantity (function output) changes with respect to change in another quantity (function input). It represents the slope of the secant line between two points on a function graph.

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
• \( b \) — Second point on x-axis
• \( a \) — First point on x-axis

Explanation: The formula calculates the average rate of change between two points on a function, which represents the slope of the secant line connecting 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 to the derivative concept.

4. Using the Calculator

Tips: Enter function values at points a and b, and the x-coordinates of these points. Ensure b ≠ a to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: How is rate of change different from derivative?
A: Rate of change is the average change over an interval, while derivative is the instantaneous rate of change at a point (limit as interval approaches zero).

Q2: What does a negative rate of change indicate?
A: A negative ROC means the function is decreasing between points a and b - the output decreases as input increases.

Q3: What are typical units for rate of change?
A: Units are "output units per input unit" (e.g., meters/second for position vs. time).

Q4: Can ROC be calculated for non-linear functions?
A: Yes, ROC works for any function, but represents the average slope between two points (may vary across different intervals).

Q5: How does ROC relate to real-world applications?
A: ROC appears everywhere: speed (distance/time), inflation rate (price/year), reaction rates (concentration/second), etc.