Lesson Plan: Critical Points and Local Extrema of a Function Mathematics • Higher Education

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find critical points of a function and check for local extrema using the first derivative test.

Objectives

Students will be able to

  • recall the definition of a critical point of a function,
  • find the critical points of a function,
  • understand that critical points can be classified as minima, maxima, and points of inflection,
  • classify a critical point as a local minimum or maximum using the first derivative test.

Prerequisites

Students should already be familiar with

  • differentiation (including the chain, product, and quotient rules),
  • the concept of continuity (not necessarily the formal definition).

Exclusions

Students will not cover

  • absolute extrema,
  • infimum and supremum,
  • second derivatives.

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