Practice question · Match the pairs
Match each concept to its definition.
- Critical point
- Hessian
- Saddle point
- Concavity
- Matrix of second partial derivatives
- Neither max nor min, up in one direction, down in another
- Surface curves downward, ensures a maximum
- Where all first partial derivatives are zero
Hints
- One condition finds candidates; the other classifies them.
- One term names the matrix of second derivatives.
Show the answer
- Critical point → Where all first partial derivatives are zero
- Hessian → Matrix of second partial derivatives
- Saddle point → Neither max nor min, up in one direction, down in another
- Concavity → Surface curves downward, ensures a maximum
Why
Find candidates (FOC), test them (Hessian), interpret the geometry (saddle vs extremum).
Practise Unconstrained Multivariable Extrema
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