# How does instantaneous rate of change differ from average rate of change?

##### 1 Answer

Aug 4, 2014

Instantaneous rate of change is essentially the value of the derivative at a point; in other words, it is the slope of the line tangent to that point. Average rate of change is the slope of the secant line passing through two points; it gives the average rate of change across an interval.

Below is a graph showing a function,

#(Deltay)/(Deltax) = (f(4) - f(2))/(4 - 2)#

is the average rate of change of

Below is a graph showing the function

#dy/dx = f'(2) = 2*2 = 4# ,

and it is the instantaneous rate of change at the point