Average Rate of Change Calculator
Find the average rate of change of a function f(x) between two x-values, with f(a), f(b) and the working.
Change the values and press Calculate to work out your own figures.
Enter f(x) and two x-values.
Show the working
- f(x) = x^2
- f(2) = 4 and f(3) = 9
- (f(b) − f(a)) ÷ (b − a) = (9 − 4) ÷ (3 − 2) = 5 ÷ 1 = 5
How to use it
Enter f(x) and two x-values.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
(f(b) − f(a)) ÷ (b − a)
Slope of the secant
The average rate of change is the slope of the line through (a, f(a)) and (b, f(b)).
Questions
What is the average rate of change of x² from 2 to 3?
(9 − 4) ÷ (3 − 2) = 5.
Formulas
(f(b) − f(a)) ÷ (b − a)
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).