Average Rate of Change

Given a function  plotted in the Cartesian plane as , the average rate of change (or average rate of change function) of  from  to  is given by

This corresponds the the slope of the secant line connecting the points  and .

The limiting value

as the point  approaches  gives the instantaneous slope of the tangent line to  at each point , which is a quantity known as the derivative of , denoted  or .