ABSTRACT
Another application of the above discussion is in the multivariable calculus. The quadratic term in the Taylor expansion of a multivariable function at a critical point (which may be, by shifting the origin, assumed to be the origin) determines the nature of the critical point. If we can reduce it to λ1x
2 1 + · · ·+ λnx2n, we can infer the nature of the critical point by looking at
the signs of λ1, . . . , λn.
