Application of derivatives in real life examples with solutions

8-1 Discussion: Use of Derivatives Discuss a real-world application of the use of calculus-based derivatives for maximizing profits. In response to your peers, comment on the example provided and its fit within the concept. NOTE: One to two paragraphs written in APA format. Reference scholarly or peer-reviewed sources to support your discussion points, as appropriate. First Peer Response: Michael McEntire posted Apr 2, 2018 10:05 PM The derivative function can be used to demonstrate the “rate of change [which] can be interpreted as marginal cost, marginal revenue, or marginal profit” dependent on what the original function represents (Lial, 2011). As I work in healthcare, two examples that I have seen graphed are healthcare expenditures per individual and prescription drug expenditures. It’s important to both review historical trends and forecast future projections, as “forecast[s] provides valuable information to help guide [financial and] strategic planning efforts” (Schumock, 2015). The profit function (f(x) = 3x 2 + 2x + 1) may be used to determine maximum profit. First, one must find the first derivative of the equation: 3x 2 + 2x + 1 would become 6x + 2. Then set the first derivative to equal zero: 6x + 2 = 0. Solve for x: x = 1/3. Substitute the value of x in the original equation: 3(1/3) 2 + 2(1/3) + 1 = 3/9 + 2/3 + 1 = 1/3 + 2/3 + 1 = 2. In my given example of pharmaceutical prices above, one would also want to evaluate revenue and cost functions to ascertain how the bottom line of a given business relates to prescription expenditures overall. Reference Lial, M. L., Hungerford, T. W., & Holcomb, J. P. (2011). Mathematics with applications in the management, natural, and social sciences.Upper Saddle River, NJ: Pearson. Schumock, G. T., Li, E. C., Suda, K. J., Wiest, M. D., Stubbings, J., Matusiak, L. M., & ... Vermeulen, L. C. (2015). National trends in prescription drug expenditures and projections for 2015. American Journal Of Health-System Pharmacy, 72(9), 717-736. doi:10.2146/ajhp140849 Second Peer Response: Nicole Weber posted Apr 2, 2018 11:36 AM To understand how we use calculus derivatives in the real world we need to understand what calculus is. To begin, calculus provides a language for economists and allows them to illustrate solving problems. More importantly, it has a very important role illustrating the principal of economics. Calculus primarily focuses on functions and derivatives. Functions examine the relationship between two or more variables. Contrariwise, derivatives consider the rate of change from one variable to another and how they relate. Therefore, both functions and derivatives related to the most important concepts of economics. Therefore, in the real world a company may use calculus to research and examine relationships of one account to another. When we speak in terms of math, those variables are represented by X and Y. Simply put, if the value of X changes the value of Y then they have a functional relationship. In the real world an example would be education and employment. If there is a rise in employment as years of education and experience increase then there is a positive relationship. This information allows economists to process different variables that may affect their company. Hall, Shane. (2017). How is calculus used in economics? Pocket Sense. Retrieved from: https://pocketsense.com/calculus-used-economics-2776.h ...