Introduction to Applications of the Derivative

In business, companies are interested in maximizing revenue. Consider a scenario in which a company has collected data on how many cars it is able to lease depending on the price it charges its customers to rent a car. The company would then use the data to determine the price the company should charge to maximize the amount of money it brings in (see “Chapter Opener: Maximizing Revenue” Example in Section 3.3: Applied Optimization).

Being able to solve this type of problem is just one application of derivatives introduced in this chapter. We also look at how derivatives are used to find the maximum and minimum values of a function. As a result, we will be able to solve applied optimization problems, such as maximizing revenue and minimizing cost for a certain area. In addition, we examine how derivatives are used to provide accurate graphs of functions and solve problems that involve two related quantities that change over time.

Introduction from Calculus, Volume 1, by Strang and Herman, OpenStax (Web), licensed under a CC BY-NC-SA 4.0 License.