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 to 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 
.
