# Classroom Activities

• ##### Subject Area

• Math: Calculus: Applications of the Derivative

9-12

40 Minutes

• ##### Device

TI-83 Plus Family,TI-84 Plus Family

TI Connect™

• ##### Other Materials
You'll need to use TI Connect to transfer this data, but you could select other sets by importing data from the website into Excel.
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Using Traffic Data to Reinforce Inflection Points in Calculus

Published on 03/20/2007

#### Activity Overview

Real data from the morning rush on the Chicago expressways is the basis for a piece-wise regression. The students' success depends on their understanding of inflection points. Students need to use the Select command to split the data into portions to perform the regressions.

#### Before the Activity

Students will be more interested in the activity if they have a chance to examine the problems caused by excessive traffic and waiting. You could discuss the pollution, wasted fuel, stress to drivers, and wasted time that result from poor traffic planning. Next set up a stat plot with traf list in L2. Use the seq(x,x,1,79) command in L1 to create an ordered list to match the L2 data. Examine the morning rush and try to estimate the times that were the busiest. Also, students should examine concavity for each interval.

#### During the Activity

Examine the data with the students. When are the times increasing and decreasing? Are there any local maximums or minimums? Absolute max and mins? Where is the graph concave up/down? Follow the PowerPoint directions to select data and use quadratic regressions one piece at a time.

#### After the Activity

Give the students a new set of traffic data and let them calculate the regressions on their own. Students can clear L1 and L2 and then analyze the trajam data from the attached list. You can find more traffic data at GCM Travel Stats. www.gcmtravelstats.com

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