Pattern 1: Piecewise Parameter Finding (High Frequency) Given f with parameters, find values for continuity/differentiability. Typically 2 unknowns, 2 equations.

Pattern 2: Points of Non-differentiability (High Frequency) Given |polynomial| or max/min functions, count corners. Each simple zero of the polynomial inside || gives one corner.

Pattern 3: Rolle's/LMVT Verification (Moderate) Verify hypotheses, find the c. Or use these theorems to prove inequalities.

Pattern 4: IVT for Root Existence (Moderate) Show sign change for existence, use monotonicity for uniqueness.

Pattern 5: $x^n$ sin$\frac{1}{x}$ Type (Moderate) Test continuity and differentiability at origin. n >= 2: differentiable. n = 1: not differentiable. Always continuous for n >= 1.

Pattern 6: Floor/Ceiling Compositions (Low-Moderate) Count discontinuities of [f(x)] or analyze continuity of composite involving [x].