Calculus: Derivative Project Ideas

AP Calculus AB is typically the highest course for many high school students. Coming up with a possible Calculus project has been challenging. Not because the course is hard. It has been challenging because my desire to keep the project authentic and connected to the major concepts of the subject. Every time I create a project, I want it to be real-world work. I also want to have students think deeply about the "power standards" of the subject.

Identifying the power standards for Calculus was simple. I agree with Steve Strogatz's post in The NY Times,  "Calculus is the mathematics of change. The subject is gargantuan - and so are its textbooks. But within that bulk you'll find two ideas shining through. Those two ideas are the 'derivative' and the 'integral'."  Although knowing that a project on derivates or integrals was easy to identify, the real world application of it has been much harder. Every time I run into a person whose profession is mathematics based such as an engineer, I would ask them how do they use calculus in their work. They would often laugh and say they don't. 

Despite these roadblocks, I am determined to find an authentic use of calculus in the workplace. After searching, I think I have some ideas for a derivative project. The main criteria I am using in thinking of ideas is that there are multiple solutions. Please let me know what you think of them and please add other possible projects in the comments below. 

• Drug Flow: Healthcare is huge topic today. It is a constant discussion at dinner tables. One aspect of healthcare is drugs. Many people do not understand the affects of these on the body. The Center for Policy Analysis wants to educate the public on how various drugs affects the body so that people will be more empowered about their health care. They want to explain their website to include this information. It must include how to calculate the effects in layperson's terms (idea is adapted from extended applications in Calculs with Applications by Lial, Greenwell and Ritchey).
• Classic Box: Kellogg is in the process of repackaging their cereal boxes to respond to market demands. Increase in gas over the last decade has caused the company to increase the cost of cereal. However, recent changes in tax code is lowering Americans ability to pay increases in cereal. The company wants to redesign the boxes to achieve maximum volume but cost less to produce. The company's director of product development is requesting a proposal to meet the company's needs. It must include calculations of the cost to produce and the volumes of the new products (idea is adapted from the classic box problem in most calculus textbooks. There is also an activity by TI-Instruments with their TI-Nspire calculator).
• Start-up Company: Terri Miller has left her position as a manger of a local company to start her own business. She makes lady handbags. The demand has really taken off and she is in full production. She needs to get more capital to expand but that requires creating a proposal that details various financial aspects of the business. Investors are wanting a lot of information including her marginal cost, revenue and profit for the organization. She is small and don't have the staffing to help with the creation of this document. She is seeking assistance to help grow her business (idea is adapted from Calculs with Applications by Lial, Greenwell and Ritchey).