Differentiability vs Continuity Relationship
About This MicroSim
This interactive Venn diagram visualizes the important relationship between differentiability and continuity:
- Differentiable functions form a subset of continuous functions
- Continuous but not differentiable functions exist (corners, cusps)
- Discontinuous functions are always non-differentiable
Key Concepts
| Statement | Truth Value |
|---|---|
| Differentiable ⟹ Continuous | TRUE |
| Continuous ⟹ Differentiable | FALSE |
| Not Continuous ⟹ Not Differentiable | TRUE |
How to Use
- Click on regions of the Venn diagram to see examples
- Hover over functions to see their graphs
- Explore each category to understand why functions belong there
Learning Objectives
- Explain why differentiability implies continuity but not vice versa (Bloom Level 2: Understand)
- Classify functions by their differentiability and continuity properties