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Lesson Plan: Concavity and Points of Inflection Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine the concavity 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 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.
