# Rate of Change of a Function

## Rate of Change of a Function

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.