Lesson: Concavity and Points of Inflection Mathematics • Higher Education

In this lesson, we will learn how to determine the concavity of a function as well as its inflection points using its second derivative.

Lesson Plan

Objectives

Students will be able to

  • understand how the second derivative of a function relates to its concavity and how to apply the second derivative test,
  • find the intervals over which a function is concave upward or concave downward,
  • understand the relationship between inflection points and concavity,
  • find the inflection points of a function.

Prerequisites

Students should already be familiar with

  • differentiation,
  • finding critical points,
  • the concept of continuity (not necessarily the formal definition).

Exclusions

Students will not cover

  • analysis in cases where the second derivative does not exist.

Lesson Video

Video Thumbnail
17:22

Lesson Explainer

Sample Question Videos

  • 04:37
  • 06:14
  • 04:07

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