Module 4 : Local / Global Maximum / Minimum and Curve Sketching
Lecture 12 : Asymptoes [Section 12.1]
Thus, for , and hence is concave up for . For , and hence is concave down for . Thus, is a point of inflection. Its is easy to check that has a local maximum at and local minimum at .
12.1.6
Remark:
Consider a rational function such that ,
where and are polynomial functions with and
, and hence 
is concave up for 
. For 
, and hence 
is concave down for 
. Thus, 
is a point of inflection. Its is easy to check that 
has a local maximum at 
and local minimum at 
. 
such that 
, 
and 
are polynomial functions with 
and 
. 
by 
, we can write 
, 
