PAU Matemáticas II CV Junio 2026 | Problema 4.1: Análisis de funciones paso a paso

In this video, we solve Problem 4.1 from the Mathematics II exam of the Valencian Community University Entrance Exams (PAU) in June 2026, corresponding to the function analysis section. We work with the function f(x) = (x + 1)/(x^2 + 1) and study its main characteristics step by step: domain, continuity, asymptotes, intervals of increase and decrease, maxima, minima, and graphing. 📌 In this video you will see: How to calculate the domain of a rational function. How to study the continuity of the function. How to analyze whether vertical asymptotes exist. How to calculate the horizontal asymptote. How to differentiate a rational function. How to study intervals of increase and decrease. How to calculate relative maxima and minima. How to determine if relative extrema are also absolute extrema. How to graph the function using its key points. Main Results: The domain of the function is R. The function is continuous throughout its domain. It has no vertical asymptotes. The horizontal asymptote is y = 0. The function is decreasing on (-∞, -1 - √2) and (-1 + √2), +∞). The function is increasing on (-1 - √2), -1 + √2). It has a relative and absolute minimum at (-1 - √2), (1 - √2)/2). It has a relative and absolute maximum at (-1 + √2), (1 + √2)/2). This exercise is very useful for reviewing function analysis, rational functions, domain, continuity, limits, asymptotes, derivatives, increasing and decreasing intervals, relative extrema, absolute extrema, and graphing—fundamental content in Mathematics II for the second year of Bachillerato (Spanish pre-university studies) and university entrance exams. 💙 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 videos and exclusive benefits:    / @angelcuesta