Continuities of Functions
Introduction
This section is mostly the analysis of functions represented graphically. Using derivatives we find critical values. Using double derivatives we calculate inflection points.
Definitions:
Critical Value: A point on the graph of a function where either the slope is zero (f` = 0) or there is a break in the line (discontinuous).
Inflection Point: A point on the graph of a function where its curvature changes sign. This is also referred to as a change in concavity (f`` = 0).
For example:
1.1 
a) Find 
b) Factor and find critical values.
set = 0 because critical values are found when 
c) Give the intervals of increase and decrease.
pick any points to test. They must be in the intervals made by the critical values.
14
a positive 
indicates the function is increasing
A negative indicates the function is decreasing
a positive indicates the function is increasing
Increasing:
Decreasing:
d) Give the coordinates of the relative minimum.
The relative minimum will be the critical value which follows the interval of decrease on the graph.
(3, -13.5)
e) Give the coordinates of the relative maximum.
