Practice question · Multiple choice
A saddle point is a maximum in one direction and a minimum in another. Why does a manager who tests only one direction confidently reach the wrong conclusion?
Hints
- Picture a mountain pass. Walk along the ridge and then across it.
- Ask what a single cross-section of a surface can and cannot reveal.
Show the answer
B. Because a one-dimensional test cannot see perpendicular fall
Why
Walk the pass one way and you are at a summit; turn ninety degrees and you are at the bottom of a valley, one cross-section cannot distinguish those cases. The Hessian determinant is the test that examines curvature in every direction simultaneously, which is why the SOC is a matrix condition rather than a sign.
Practise Unconstrained Multivariable Extrema
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More questions on Unconstrained Multivariable Extrema
- Which conditions guarantee a local maximum at a critical point?
- A saddle point is a critical point where the function is a maximum in one direction and a minimum in another.
- Complete the Hessian test.
- Order the steps of finding and classifying a multivariable extremum.
- Match each concept to its definition.
- For f(x,y) = x² - y², the origin is a critical point. fxx = 2, fyy = -2, fxy = 0. The determinant is: