Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 :  Absolute maxima / minima [Section 39.1]
39 .1 Absolute maxima/minima
   
39.1.1 Definition:
 

Let If there exists a point such that

then the number is called the absolute maxima of in Similarly, if there exists a point such that

then the number is called the absolute minima of in

   
39.1.2 Note:
  Recall that If is closed and bounded, and is continuous, then by theorem 30.2.4, both absolute maxima and absolute minimum exist.
   
39.1.3 Theorem:
 

Let

(i)
 Let assume its absolute maximum at a point Then, either at is a boundary point of or is a critical
point of in .
(ii)
 Let assume its absolute minimum at a point Then, either is a boundary point of or is a critical
  point of in .
 
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