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stationary point


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(in two variables)

A point P on the surface z=f(x, y) is a stationary point if the tangent plane at P is horizontal. This is so if f/x=0 and f/y=0. Now let

If rt>s2 and r < 0, the stationary point P is a local maximum (all the vertical cross-sections through P have a local maximum at P). If rt>s2 and r>0, the stationary point is a local minimum (all the vertical cross-sections through P have a local minimum at P). If rt < s2, the stationary point is a saddle-point.

Subjects: Mathematics.


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