1. What is Rate of Change?

The rate of change (ROC) measures how much a quantity changes between two points. In this calculator, we specifically calculate the average rate of change between x=3 and x=5.

2. How Does the Calculator Work?

The calculator uses the rate of change equation:

Where:

• \( f(5) \) — Function value at x=5
• \( f(3) \) — Function value at x=3
• ROC — Rate of change (units per unit)

Explanation: The equation calculates the slope of the secant line between the points (3, f(3)) and (5, f(5)).

3. Importance of Rate of Change

Details: Rate of change is fundamental in mathematics and sciences for understanding how quantities change relative to each other. It's used in physics (velocity), economics (marginal cost), and many other fields.

4. Using the Calculator

Tips: Enter the function values at x=5 and x=3. The calculator will compute the average rate of change between these two points.

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 (like this calculator does), while instantaneous ROC measures change at a single point (using derivatives).

Q2: Can I use this for non-linear functions?
A: Yes, this calculates the average rate of change between two points, regardless of the function's shape.

Q3: What does a negative ROC indicate?
A: A negative ROC means the function is decreasing between x=3 and x=5.

Q4: How is this different from slope?
A: For linear functions, ROC and slope are identical. For non-linear functions, ROC gives the slope of the secant line between two points.

Q5: Can I change the interval from 3-5 to something else?
A: This specific calculator is designed for the 3-5 interval. For other intervals, you would need a different calculator.