Lesson Plan: The Differentiability of a Function Mathematics • Second Year of Secondary School

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.