Calculus Assignment: Analysis of Energy Consumption and Revenue

This calculus assignment delves into the analysis of energy consumption and revenue functions. The solution begins by addressing energy consumption, utilizing integration and derivatives to determine local maxima and derive a function representing the consumption over time. It involves solving a system of linear equations to find coefficients and testing the function against given conditions. The second part focuses on revenue functions, calculating derivatives, identifying critical points, and determining the global maximum. The assignment explores factors impacting revenue generation, emphasizing the importance of strategic decisions and market preferences. Furthermore, it analyzes how adjustments to the revenue function can lead to increased equilibrium revenue. The provided solutions demonstrate a comprehensive understanding of calculus principles, including function analysis, optimization, and the application of mathematical concepts to real-world scenarios.