Lesson Plan: The Differentiability of a Function Mathematics • Higher Education

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine whether a function is differentiable and identify the relation between a function’s differentiability and its continuity.

Objectives

Students will be able to

  • understand the definition of the differentiability of a function at a point,
  • understand the definition of the differentiability of a function over an interval,
  • understand the relationship between the differentiability and the continuity of a function,
  • determine whether a given function is differentiable at a point (or over an interval),
  • recognize and classify the cases where a function is not differentiable at a point, including
    • discontinuities,
    • corners,
    • cusps,
    • vertical tangents,
    • cases of oscillating behavior.

Prerequisites

Students should already be familiar with

  • continuity,
  • limits (including one-sided limits),
  • the power rule of differentiation.

Exclusions

Students will not cover

  • implicit differentiation.

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