Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 37 :  Maxima and Minima [Section 37.1]
 
        Figure 2. Locale minimum at
  For functions of three or more variables, the concepts of local maximum/minimum can be defined similarly. Further, similar to function of one variable, we have the following sufficient condition for a point to be a point of local maximum/minimum.
 

 
37.1.3 Theorem (Necessary conditions for local extremum or point):
 

Let be any unit vector.

(i)
If has a local maximum/local minimum at and exists,
 

then

(ii)

If both and exist and has a local maximum or a local

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