4.2 The Shape of a Graph by SGLee - HSKim - JHLee
1-5. Find the local maximum and minimum values of 
. In addition, find the intervals on which 
is increasing and decreasing,
and the intervals of concavity and the inflection points, sketch a graph of 
.
1. 
.
http://matrix.skku.ac.kr/cal-lab/cal-4-2-1.html
(a) local maximum: 
local minimum: 
(b) increasing on 
decreasing on 
(c) inflection point at 
concave down on 
concave up on 
2. 
.
5. 
In addition, find intervals in which the graph of 
is concave upward or concave downward.
, 
9. 
, inflection point at 
.
and 
.
using the following information.
.
and intervals of concavity.
, 
, 
and 
and 
; 
and 
has 
different roots.
. Then will have one local maximum and one local minimum. There will be 
roots if and only if the maximum is positive and the minimum is negative.
and 
.
and 
. Hence 
has local maximum at 
and local minimum at 
. Therefore, if 
there will be 
roots.
for which 
for all real 
.
, 
.
so that 
has two
and so 
, 
and so 
.
.
and 
.
.
using (a) and (b).
, 
and 
be increasing functions. Prove that 
is increasing function.
, 
, 
is increasing.
on an interval 
then 
is increasing on 
.
is concave upward on 
.
25. Use CAS to find 
and 
when 
.
26. Let 
. Find the local maximum, minimum values and inflection points of 
. Sketch the graph of 
.
27. Let 
. Find the local maximum, minimum values and inflection points of 
.
