Modul
e
4
: Local / Global Maximum / Minimum and Curve Sketching
Lecture
12 : Curve sketching [Section 12.2]
12.2.8
Let us sketch the curve
. We make the following observations:
(i)
is defined for every
.
(ii)
is differentiable for all
.
(iii)
For
. Thus the curve passes through
.
(iv)
Thus,
is an odd function.
(v)
Since
is a strictly increasing function. Further
. Thus
is the only critical point. However,
is neither a local maxima, nor a local minima.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
. We make the following observations: 
is defined for every 
. 
is differentiable for all 
.
. Thus the curve passes through 
. 
Thus, 
is an odd function. 
is a strictly increasing function. Further 
. Thus 
is the only critical point. However, 
is neither a local maxima, nor a local minima. 
