PAU Valencian Community – Mathematics CCSS: Problem 2A (July 2025-Extra DANA) | step by step

In this video, we solve Problem 2A from the Applied Mathematics for Social Sciences II (MACS II) exam of the Valencian Community University Entrance Exams (PAU/EBAU) – July 2025 Extra Session (DANA Extra). 🎁 Problem situation: An agricultural company that grows tropical fruits uses an automated irrigation system. The daily water requirement, in cubic meters per day, is given as a function of the number of days of growth x (from 0 to 30) by a piecewise-defined function: From 0 to 8 days: f(x) = x^3 − 4x^2 + 10 From more than 8 days to 20 days: f(x) = 3x + 9 From more than 20 days to 30 days: f(x) = 70 📌 Exercise questions: a) Study the continuity of the function over the entire interval from 0 to 30 days. b) Determine on which days the water requirement is maximum and minimum. c) Calculate the area bounded by the function and the x-axis between days 3 and 7. 🚀 WHAT YOU WILL LEARN IN THIS VIDEO • Analyze piecewise-defined functions without domain errors. • Study continuity at points where the expression changes. • Calculate absolute maxima and minima on a closed interval. • Interpret results in a real-world context. • Calculate areas using definite integrals. • Solve a typical mathematical analysis exercise from the university entrance exam (PAU). 👍 If you found this video helpful, please like, subscribe, and share it. ✍️ Leave any questions or exercises you'd like to see solved in the comments. 💙 If you'd like to support the channel: Bizum: 621007935 https://paypal.me/angelcuesta1972 📲 Follow me on social media:   / angel-cuesta-115048070199431     / profesorencasa1   👥 Become a channel member to access full content and exclusive benefits:    / @angelcuesta