Differentiability Checker
About This MicroSim
This interactive tool guides you through the systematic process of checking whether a function is differentiable at a point.
The Differentiability Checklist
- Is f(a) defined? The function must have a value at the point
- Is f continuous at a? The limit must equal the function value
- Compute f'₋(a) - the left-hand derivative
- Compute f'₊(a) - the right-hand derivative
- Are they equal and finite? Both one-sided derivatives must match
How to Use
- Select a function from the preset buttons (A-E)
- Click "Step Through" to advance one step at a time
- Or click "Auto Check" to see all steps automatically
- Watch the checklist populate with ✓ or ✗ for each step
- See the final verdict: Differentiable or Not Differentiable (with reason)
Test Functions
| Function | Type | Expected Result |
|---|---|---|
| f(x) = x² | Smooth | Differentiable |
| f(x) = |x - 1| | Corner | Not differentiable at x = 1 |
| f(x) = x^(2/3) | Cusp | Not differentiable at x = 0 |
| Jump function | Discontinuity | Not differentiable |
| f(x) = ∛x | Vertical tangent | Not differentiable at x = 0 |
Learning Objectives
- Apply a systematic process to determine differentiability (Bloom Level 3: Apply)
- Identify the reason when differentiability fails