Rate of Change Formula:
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Definition: This calculator computes the average rate of change of a function between two points.
Purpose: It helps students, engineers, and mathematicians analyze how a quantity changes relative to another.
The calculator uses the formula:
Where:
Explanation: The difference in function values is divided by the difference in input values to find the average rate of change.
Details: Rate of change is fundamental in calculus, physics, economics, and engineering for analyzing trends, velocities, and growth rates.
Tips: Enter the function values at two points (f(b) and f(a)) and their corresponding input values (b and a). The difference (b - a) cannot be zero.
Q1: What does the rate of change represent?
A: It represents the average slope of the function between two points, showing how much the output changes per unit change in input.
Q2: Can I use this for non-linear functions?
A: Yes, but it gives the average rate over the interval, not the instantaneous rate at a point.
Q3: What if b - a equals zero?
A: Division by zero is undefined. The calculator won't compute if the input values are equal.
Q4: How is this different from derivative?
A: This gives average rate over an interval, while derivative gives instantaneous rate at a point.
Q5: What units does the result have?
A: The result is unitless when all inputs are unitless, otherwise it's (units of f) per (units of x).