References: Differentiability

1. Differentiable function - Wikipedia - Formal definition of differentiability, relationship to continuity, and examples of non-differentiable functions. Core reference for the theoretical foundations in this chapter.

2. Weierstrass function - Wikipedia - Famous example of a continuous everywhere but nowhere differentiable function. Illustrates the subtle distinction between continuity and differentiability explored in this chapter.

3. Lipschitz continuity - Wikipedia - Covers conditions stronger than continuity related to differentiability, providing deeper context for understanding the differentiability-continuity relationship.

4. Calculus: Early Transcendentals (9th Edition) - James Stewart - Cengage Learning - Section 2.8 discusses when derivatives fail to exist including corners, cusps, and vertical tangents with clear visual examples.

5. Calculus (3rd Edition) - Michael Spivak - Publish or Perish - Chapters 9-10 provide rigorous treatment of differentiability conditions and the proof that differentiability implies continuity.

6. Differentiability and Continuity - Paul's Online Math Notes - Explains the relationship between differentiability and continuity with examples of functions that are continuous but not differentiable.

7. Differentiability at a Point - Khan Academy - Interactive lessons on identifying where functions fail to be differentiable, with practice problems aligned to AP curriculum.

8. Non-Differentiable Functions - Professor Leonard - Detailed lecture on corners, cusps, vertical tangents, and discontinuities as sources of non-differentiability.

9. When Derivatives Don't Exist - Math is Fun - Visual gallery of non-differentiable points with interactive graphs, complementing the chapter's Non-Differentiable Gallery MicroSim.

10. Differentiability vs Continuity - Whitman College Calculus - Open-source section covering the precise conditions for differentiability with proofs and exercises.