Modul
e
4
: Local / Global Maximum / Minimum and Curve Sketching
Lecture
12 : Curve sketching [Section 12.2]
(ii)
is defined for all real
, with
exists for all
except at
. Further
.The second derivative
is such that
.
2.
Sketch the following curves after locating intervals of increase/ decrease, intervals of concavity upward/ downward,
points of local maxima/ minima, points of inflection and asymptotes. How many times and approximately where does the curve cross the x-axis?
(i)
(ii)
(iii)
.
(iv)
.
(v)
(vi)
3.
Find constants
such that the function
has a local maximum at
a point of inflection at
and satisfy
.
4.
Given
find all
at which
has a local maximum, a local minimum or a point of inflection.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
is defined for all real 
, with 
exists for all 
except at
. Further 
.The second derivative 
is such that 
. 
. 
.
such that the function 
a point of inflection at 
and satisfy 
. 
at which 
has a local maximum, a local minimum or a point of inflection. 
