Module 4 : Local / Global Maximum / Minimum and Curve Sketching
Lecture 11 : Absolute Maximum / Minimum [Section 11.1]
(ii)
Even if a function has a local maximum at a point and exists, it need not imply that . For example consider the function for . It has local (in fact global) minimum at the point .
has a local maximum at a point 
and 
exists, it need not imply that 
. For example consider the function 
for 
. It has local (in fact global) minimum at the point 
.
