Concavity, Inflection Points, Second Derivative Test

In this video, we explore concavity, the Second Derivative, and inflection points to better understand the shape and behavior of functions in calculus. We begin by breaking down concavity and how it relates to both the first and second derivatives, connecting increasing/decreasing behavior with whether a graph is concave up or concave down. Next, we focus on inflection points, learning how to find them and how they occur where the second derivative changes sign. After building the concepts, we work through four detailed examples step-by-step. In the final example, we bring everything together by: Finding critical points, Using the First Derivative Test to determine intervals of increase and decrease, Identifying local maxima and minima, Analyzing concavity and confirming inflection points. This video is perfect for Calculus students who want a clear, structured approach to understanding concavity and applying derivative tests with confidence. Thank You for your Support! Patreon: https://www.patreon.com/cw/LinzeyGMath For Practice: https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-6b/e/analyze-points-of-inflection-algebraic #learnmath #practicemaths #maths