Avon High School
AP Calculus AB
Name ______________________________________
Period _____
Score ______ / 10
HW 3.6 – Curve Sketching & Function Analysis
1.) For each term in the top row, determine if it is applicable at the x-values a-m by placing an X in the box.
Critical
Point
Relative
Minimum
Relative
Maximum
Inflection
Point
a
b
c
d
e
f
g
h
i
j
k
l
m
2.) You are given a graph of f '( x) . Draw a picture of a possible f ( x ).
Absolute
Maximum
Absolute
Minimum
3.) You are given a graph of f '( x) . Draw a picture of a possible f ( x ).
4.) Draw a graph of f ( x)  x 4  6 x3  12 x 2  8 x  1 showing/analyzing all significant features.
.
5.) Draw a graph of f ( x) 
x2  3
showing/analyzing all significant features.
x3
6.) Draw a graph of f ( x)  cos x  x showing/analyzing all significant features.
7.) Draw a graph of f ( x) 
1
1
 2  4 showing/analyzing all significant features.
x
x