# What is the relationship between the Average rate of change of a fuction and derivatives?

##### 1 Answer

Sep 19, 2014

The average rate of change gives the slope of a secant line, but the instantaneous rate of change (the derivative) gives the slope of a tangent line.

Average rate of change:

Instantaneous rate of change:

Also note that the average rate of change approximates the instantaneous rate of change over very short intervals.