For a continuous function f that's continuous over the interval [a,b] within its domain, this applet allows for students to see/conclude that:
1) The difference quotient of a function (evaluated from x = a to x = b)
2) The average rate of change of a function (evaluated from x = a to x = b), &
3) The slope of the secant line (passing through [(a,f(a)) & (b,f(b))] drawn through f's graph
are all equivalent values.