Lesson Plan: Convexity and Points of Inflection | Nagwa Lesson Plan: Convexity and Points of Inflection | Nagwa

# Lesson Plan: Convexity and Points of Inflection Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine the convexity of a function as well as its inflection points using its second derivative.

#### Objectives

Students will be able to

• understand how the second derivative of a function relates to its convexity and how to apply the second derivative test,
• find the intervals over which a function is convex upwards or convex downwards,
• understand the relationship between inflection points and convexity,
• 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.