## Quick Reference

(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*>*s*^{2} 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*>*s*^{2} 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* < *s*^{2}, the stationary point is a saddle-point.

*Subjects:*
Mathematics.

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