Taxa de Variação Média
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
TVM
About this calculator
The Average Rate of Change (ARC) calculator determines the average rate of change of a function over an interval [a, b]. The formula used is (f(b) - f(a)) / (b - a). This value represents the slope of the secant line connecting the points (a, f(a)) and (b, f(b)) on the function's graph. It is an essential tool for understanding the average behavior of a function between two points.
To use the calculator, you enter the function expression f(x), the starting value a, and the ending value b. The system computes f(a) and f(b) and applies the ARC formula. The result is displayed as a decimal number. This tool is useful for calculus students checking exercises or for professionals analyzing rates of change in experimental data.
ARC is applied in various contexts, such as physics for average velocity, economics for average variation in costs or revenues, and engineering for analyzing growth rates. Remember that ARC provides an average, not an instantaneous rate. For instantaneous rates, use the derivative.
Cautions when using: ensure the function is defined on the interval [a, b] and that a is different from b. The calculator assumes a and b are real numbers. If the function has discontinuities in the interval, the result may not represent the actual variation. Always verify that the interval makes sense for the problem.
Frequently asked questions
What does a negative Average Rate of Change mean?
It means the function decreased on average over the interval, i.e., f(b) is less than f(a).
Does the calculator accept trigonometric functions?
Yes, you can use functions like sin(x), cos(x), tan(x) as long as they are written in a recognized format (e.g., sin(x)).
Can I use the calculator for multivariable functions?
No, the calculator only accepts single-variable functions in the form f(x).
What is the difference between Average Rate of Change and Instantaneous Rate of Change?
ARC is calculated over an interval and gives an average; instantaneous rate is the limit of ARC as the interval approaches zero, i.e., the derivative at a point.
What happens if I enter a equal to b?
The calculator will display an error because division by zero is not allowed. Ensure that a and b are different.