Modul
e
13 : Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture
38 : Second derivative test for local maxima / minima & saddle points [Section 38.1]
Thus, we can find points
close to
where
Hence,
has a saddle point at
Practice Exercises
(1)
Show that the following functions have local minima at the indicated points.
(i)
.
(ii)
.
(2)
Analyze the following functions for local maxima, local minima and saddle points:
(i)
(ii)
(iii)
(iv)
(3)
Let
(i)
Show that
is a critical point for
, but the second derivative test fails.
(ii)
Show that
is neither a point of local maximum nor local minimum
(iii)
Show that along every line through the origin,
has a local minimum at
(iv)
Show that along the curve
,
has a local maximum at
.
1
2
3
4
5
6
7
8
9
close to 
where 
Hence, 
has a saddle point at 
.
.
is a critical point for 
, but the second derivative test fails. 
has a local minimum at
, 
has a local maximum at 
. 
