Rate of Change of a Function
Given two values x[latex]_{1}[/latex] and x[latex]_{2}[/latex] of the domain of a function f, the rate of change of this function from x[latex]_{1}[/latex] to x[latex]_{2}[/latex] is the ratio:
[latex]\dfrac{f(x_{2})\space –\space f(x_{1})}{x_{2}\space –\space x_{1}}[/latex].
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.[latex]\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}[/latex] = 48.