Practice question · Fill in the blanks
Complete the Hessian test.
If and , the critical point is a local ______. If , it is a ______ point.
Word bank: maximum · saddle · minimum · zero
Hints
- A positive determinant separates extrema from saddles.
- The sign of one second derivative then picks between max and min.
Show the answer
If and , the critical point is a local maximum. If , it is a saddle point.
Why
Positive with negative curvature = max; negative = saddle. The test is mechanical once you compute the three second derivatives.
Practise Unconstrained Multivariable Extrema
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