Given two values x\(_{1}\) and x\(_{2}\) of the domain of a function f, the rate of change of this function from x\(_{1}\) to x\(_{2}\) is the ratio:
\(\dfrac{f(x_{2})\space –\space f(x_{1})}{x_{2}\space –\space x_{1}}\).
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.
\(\dfrac{f(x_{2})\space –\space f(x_{1})}{x_{2}\space –\space x_{1}}=\dfrac{(4 × (7)^{2}\space –\space 3)\space –\space (4× (5)^{2}\space –\space 3)}{7\space –\space 5}=\dfrac{193\space –\space 97}{2}\) = 48.