Calculate the Rate of Change of a Function

Learning Objectives

In this section, you will:

Find the average rate of change of a function.
Use a graph to determine where a function is increasing, decreasing, or constant.
Use a graph to locate local maxima and local minima.
Use a graph to locate the absolute maximum and absolute minimum.

Gasoline costs have experienced some wild fluctuations over the last several decades. Table 1 lists the average cost, in dollars, of a gallon of gasoline for the years 2005-2012. The cost of gasoline can be considered as a function of year.

$y$	2005	2006	2007	2008	2009	2010	2011	2012
$C(y)$	2.31	2.62	2.84	3.30	2.41	2.84	3.58	3.68

Table 1

If we were interested only in how the gasoline prices changed between 2005 and 2012, we could compute that the cost per gallon had increased from $2.31 to $3.68, an increase of $1.37. While this is interesting, it might be more useful to look at how much the price changed per year. In this section, we will investigate changes such as these.

Source: Rice University, https://openstax.org/books/college-algebra/pages/3-3-rates-of-change-and-behavior-of-graphs
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