Here you see part of the grph of the function .
The mean change of the function on the interval is:
The rate of change at the point can be found by calculating the difference quotient for the interval :
You continue to reduce until it approaches .
This gives you a sequence of difference quotients.
In this sequence, the value of the difference quotients will be approaching a certain value.
This value is the derivative at x = a.
It is the rate of change of the function at .
It is also the slope of the tangent at for the graph of .
You write: .
On the graphing calculator a derivative is written as dy/dx.