How does instantaneous rate of change differ from average rate of change?
1 Answer
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
http://sci.tamucc.edu/~jgiraldo/calculus1/classesguidelines/18DerivativeDefinition/DerivativeDefinitionv07.html
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
http://sci.tamucc.edu/~jgiraldo/calculus1/classesguidelines/18DerivativeDefinition/DerivativeDefinitionv07.html