Chapter 12.4, Problem 35E

Consumer Price Index The following graph shows the approximate value of the U.S. Consumer Price Index (CPI) from July 2005 through March 2006:

$I\left(t\right)$

CPI July 2005-Mar 2006

The approximating curve shown on the figure is given by

$I\left(t\right)=0.06t^3-0.8t^2+3.1t+195\left(0\le t\le 8\right),$ where t is time in months. ( $t=0$ representsJuly 2005.)

a. Locate the intercepts, extrema, and points of inflection of the curve, and interpret each feature in terms of the CPI. (Approximate all coordinates to one decimal place.) [HINT: See Example 1.]

b. Recall from Section 12.2 that the inflation rate is defined to be $\frac{I\text{'}\left(t\right)}{I\left(t\right)}$. What do the stationary extrema of the curve shown above tell you about the inflation rate?