Sketching Graphs of 1 over f
Given a functionto sketch the graph ofnote the following:
ifasthenfrom above asand ifasthenfrom below as
iffrom above asthenasand if from below asthenas
ifhas a maximum atthenhas a minimum atand ifhas a minimum atthenhas a maximum at
Ifhas a minimum atthenhas a maximum atand ifhas a minimum atthenhas a maximum at
Example:equals 0 when approaching 0 alternately from above and below.
whenand -1 whenWhenthis is a maximum forso a minimum forand whenthis is a minimum forso a maximum for
The graphs ofandare sketched below.