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