Differentiability of Piecewise Defined Functions

Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP® exam question.

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Instructional Ideas

  • Use the resource to help develop a lesson on differentiable piecewise functions
Classroom Considerations

  • Learners should be familiar with the Mean Value Theorem
  • An understanding of the definition of the derivative using limits is necessary

  • Provides complete proofs for each theorem

  • No lesson content or indication of how to use the information as part of a lesson