AP Calculus Unit 5 Lesson 4: Using the First Derivative Test to Find Relative (Local) Extrema

In this video, we dive into the First Derivative Test, a fundamental tool in calculus for analyzing the critical points of a function to determine relative (or local) maximum and minimum values. We'll start with clear definitions of relative extrema, visualizing their behavior on a graph. Then, we'll demonstrate how to apply the First Derivative Test with step-by-step examples, focusing on changes in the sign of the derivative to identify maxima and minima. Perfect for students or anyone looking to strengthen their understanding of derivatives and their applications in real-world and mathematical contexts!