Question

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

Answer 1

Instantaneous rate of change is the first derivative `d/dx` of the function. However, average rate is `(f(x)-f(a))/(x-a)`

Explanation:

Instantaneous rate of change is the definition of a derivative. In more common terminology `limh->0 (f(x+h)-f(x))/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.