Module 13 : Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 37 : Maxima and Minima [Section 37.1]
37.1.7
Example:
Consider the function
Then
Thus
gives as the only critical point of . However, at , has neither a local maximum, nor local minimum. For example, for any ,
and
Practice Exercises
(1)
Show that the following functions have local maximum at the point :
(i)
.
(ii)
.
(2)
Show that the following functions have local minimum at the indicated point:
(i)
.
(ii)
(3)
Show that the following functions have neither local maximum, nor local
minimum at
as the only critical point of 
. However, at 
, 
has neither a local maximum, nor local minimum. For example, for any 
, 
: 
.
.
.
.
.
