Module 4 : Local / Global Maximum / Minimum and Curve Sketching
Lecture 11 : Absolute Maximum / Minimum [Section 11.1]
11.1
Absolute Maximum/Minimum:
11.1.1
Definition:
Let .
(i) A point is called a point of absolute maximum for if
The value is called the absolute maxima of .
(ii) A point is called a point of absolute minimum for if
The value is called the absolute minima of .
Recall that for every continuous function there exist points in such that is absolute maximum and is absolute minimum. We shall analyze method of finding such points.
11.1.2
Definition:
For a function , a point is called a critical point of if and either is not differentiable at , or is differentiable at with .
11.1.3
Theorem:
Let be continuous. Then, assumes its absolute maximum as well as its absolute minimum at some points which are either critical point of or are the end points .
. 
is called a point of 
if 
is called the 
. 
is called a point of 
if 
is called the 
. 
there exist points in 
such that 
is absolute maximum and 
is absolute minimum. We shall analyze method of finding such points. 
, a point 
is called a 
if 
and either 
is not differentiable at 
, or 
is differentiable at 
with 
. 
be continuous. Then, 
assumes its absolute maximum as well as its absolute minimum at some points which are either critical point of 
or are the end points 
. 
