Calculate the Rate of Change of a Function

We will continue exploring functions using equations, tables, words, and graphs by finding average rates of change of functions.

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,
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