How do you find the average rate of change of a function over an interval?

The average , f(x), over the closed interval [a, b] is given by

##(f(b) – f(a))/(b – a)##

For example, to find the average rate of change of ##f(x) = x^2+3## on the closed interval [1, 3] you need to evaluate

##(f(3) – f(1))/(3 – 1) = (12 – 4)/2 = 8/2 = 4##

Again, graphically, this is the slope of the secant line through the graph of

##f(x) = x^2 + 3##

through the points (1, 4) and (3, 12). See the graph below.