Practice question · Match the pairs
Match each second derivative test outcome to the classification.
- D > 0, > 0
- D > 0, < 0
- D < 0
- Test inconclusive
- Local maximum
- Local minimum
- Saddle point
Hints
- The discriminant's sign comes first, then the sign of one second derivative.
- A negative discriminant settles the case on its own.
Show the answer
- D > 0, > 0 → Local minimum
- D > 0, < 0 → Local maximum
- D < 0 → Saddle point
- → Test inconclusive
Why
The discriminant ᵧᵧ − (ᵧ)² determines the critical point type.
Practise Optimization: Critical Points and Lagrange Multipliers
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