Modul
e
4
: Local / Global Maximum / Minimum and Curve Sketching
Lecture
11 : Convex / Concave Functions [Section 11.2]
11.2.9
Theorem (Tests for point of inflection):
Let
(i)
Let
exist in
, for some
, except possibly at
, such that
is strictly increasing in
is strictly decreasing in
or vice versa. Then,
has point of inflection at
.
(ii)
Let
exist in
, for some
, except possibly at
, such that
for
and
for
, or vice versa. Then,
has a point of inflection at
.
Proof:
Follows from theorem 11.2.6, 11.2.8 and the definition of a point of inflection.
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exist in 
, for some 
, except possibly at 
, such that 
is strictly increasing in 
is strictly decreasing in 
or vice versa. Then, 
has point of inflection at 
. 
exist in 
, such that 
for 
and
for 
has a point of inflection at 
. 
