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.
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,
- vertical tangents,
- cases of oscillating behavior.
Students should already be familiar with
- limits (including one-sided limits),
- the power rule of differentiation.
Students will not cover
- implicit differentiation.