# Lesson Plan: The Differentiability of a Function Mathematics

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.