Module 4 : Local / Global Maximum / Minimum and Curve Sketching
Lecture 11 : Absolute Maximum / Minimum [Section 11.1]
11.1.4
Method for locating absolute maximum/ minimum:
Above theorem tells us that to explore the absolute maximum/ minimum on , we need only to find the critical points of in , and compare the values of at these points.
11.1.5
Examples:
(i) Let
We note that is not differentiable at , since
.
Further,
So for . Thus, the critical points for are and
Hence, assumes its maximum at , and its minimum at and .
(ii)
Let us find local maximum/ local minimum, absolute maximum and absolute minimum of given by
on 
, we need only to find the critical points of 
in 
, and compare the values of 
at these points. 
is not differentiable at 
, since 
. 
for 
. Thus, the critical points for 
are 
and 
assumes its maximum at 
, and its minimum at 
and 
. 
given by
. 
