Net Change & Average Rate of Change Calculator
Calculation Results:
Net Change:
Average Rate of Change:
Understanding Net Change and Average Rate of Change
In calculus and algebra, understanding how functions behave over a specific interval is crucial. This calculator helps you determine two primary metrics: the absolute difference in values (Net Change) and the speed at which those values change relative to the input (Average Rate of Change).
What is Net Change?
Net change measures the total difference between the final value and the initial value of a function over a specific interval [a, b]. It does not account for what happened between those two points; it only looks at the "displacement."
Net Change = f(b) – f(a)
What is the Average Rate of Change?
The Average Rate of Change (ARoC) represents the slope of the secant line connecting two points on a graph. It tells you the average amount the function value (y) changes for every one-unit increase in the input (x).
Average Rate of Change = [f(b) – f(a)] / (b – a)
Practical Example
Imagine you are tracking the height of a plant. On day 2 (x₁), the plant is 10 cm tall (f(x₁)). On day 5 (x₂), the plant is 25 cm tall (f(x₂)).
- Net Change: 25 cm – 10 cm = 15 cm. The plant grew a total of 15 cm.
- Average Rate of Change: (25 – 10) / (5 – 2) = 15 / 3 = 5 cm per day. On average, the plant grew 5 cm every day during that period.
Key Differences
| Feature | Net Change | Average Rate of Change |
|---|---|---|
| Unit of Measure | Same as y (Output) | y per unit of x |
| Graphical Meaning | Vertical distance | Slope of secant line |
| Interpretation | Total growth/loss | Speed or velocity |