Given two values x1 and x2 of the domain of a function f, the rate of change of this function from x1 to x2 is the ratio:
f(x2) – f(x1)x2 – x1.
Example
Consider the function f defined by f(x) = 4x² − 3. We want to determine the rate of change of this function between the values 5 and 7 of its domain.
f(x2) – f(x1)x2 – x1=(4×(7)2 – 3) – (4×(5)2 – 3)7 – 5=193 – 972 = 48.