Given a function
to sketch the graph of
note the following:
-
if
as
then
from above asand if
asthenfrom below as -
if
from above asthen
asand if from below asthen
as -
if
has a maximum at
then
has a minimum atand ifhas a minimum atthen
has a maximum at -
If
has a minimum atthenhas a maximum atand ifhas a minimum atthenhas a maximum at
Example:
equals 0 when
approaching 0 alternately from above and below.
when
and -1 when
Whenthis is a maximum forso a minimum forand when
this is a minimum forso a maximum for
The graphs ofandare sketched below.
