Question

Find the average rate of change of each function on the interval specified.

Answer 1

The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by

$f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}$

So for f(x) = x² on [1, 5], the AROC of f is

$f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}$