# How do you determine the rate of change of a function?

##### 1 Answer
Mar 7, 2018

Instantaneous rate of change is the first derivative $\frac{d}{\mathrm{dx}}$ of the function. However, average rate is $\frac{f \left(x\right) - f \left(a\right)}{x - a}$

#### Explanation:

Instantaneous rate of change is the definition of a derivative. In more common terminology $\lim h \to 0 \frac{f \left(x + h\right) - f \left(x\right)}{h}$. This is described as the limit as h approaches - of the change in the function + h minus f(x). This is the distance or change in h where h is an arbitrary small number. If the limit exists a function is said to be differentiable.