Here you see part of the grph of the function .
The mean change of the function
on the interval
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.