3.6 A Summary of Curve Sketching

1
QUIZ
2
QUIZ
Extrema
Inflection Pts.
1st Derivative Test
2nd Derivative Test
3
QUIZ
Graph
4
Graph
5
3.6 A Summary of Curve Sketching

• x-intercepts and y-intercepts (P.1)
• Symmetry (P.1)
• Domain and Range (P.3)
• Continuity (1.4)
• Vertical Asymptotes (1.5)
• Differentiability (2.1)
• Relative Extrema (3.1)
• Concavity (3.4)
• Points of Inflection (3.4)
• Horizontal Asymptotes (3.5)

6
3.6 A Summary of Curve Sketching
7
3.6 A Summary of Curve Sketching
Domain
Intercepts
Asymptotes
Derivatives
Symmetry
8








(No Transcript)
9
3.6 A Summary of Curve Sketching
Guidelines
10
3.6 A Summary of Curve Sketching
Guidelines
11
3.6 A Summary of Curve Sketching
Guidelines
12
3.6 A Summary of Curve Sketching
Do on Whiteboard
Guidelines
13
3.6 A Summary of Curve Sketching
Guidelines
14
3.6 A Summary of Curve Sketching
Guidelines
15
3.6 A Summary of Curve Sketching
Guidelines
16
Graph
17
Summary
18
Determined by CNs, IPs, Vertical Asymptotes.


Und. Und. Und.

9/2 0

Und. Und. Und.

12
3
10
11
13
4
14
15
16
19
5
17
18
21
20
23
6
22
26
7
25
24
27
8
28
29
30
33
9
31
32
Use the table to finish the graph!
19
Table
20
(No Transcript)
21
3.6 A Summary of Curve Sketching
22
3.6 A Summary of Curve Sketching
23
3.6 A Summary of Curve Sketching
24
3.6 A Summary of Curve Sketching
We need 5 groups.
Group 1 2 3 4 5
p.202-3 7,27,29 9,25,31 11,28, 33 13,26, 35 21,39 37
Use the procedure demonstrated today to sketch a
graph of each function without the use of a
calculator. You may use a calculator to check
your results. Choose one of your problems and
create a poster to present. (25 points) Do your
3 problems tonight create posters tomorrow
presentations begin next week.
25
Domain
Zeros
y-int.
Asymptotes
26
(-2pi,-pi)
-pi,-pi/6
(-pi/6,5pi/6)
(3pi/2,2pi)
5pi/6,3pi/2
Critical 's
27
(-2pi,-pi)
-pi,-pi/6
(-pi/6,5pi/6)
(3pi/2,2pi)
5pi/6,3pi/2
Location of Inflection Pts.
28
F
F
F
Critical Numbers
Inflection Points








-pi,-pi/6
29
F
F
F
Critical Numbers
Inflection Points








(-2pi,-pi)
(-pi/6,5pi/6)
30
F
F
F
Critical Numbers
Inflection Points








-pi,-pi/6
5pi/6,3pi/2
31
F
F
F
Critical Numbers
Inflection Points








(3pi/2,2pi)
(-pi/6,5pi/6)
32
F
F
F
Critical Numbers
Inflection Points








5pi/6,3pi/2
33
(-2pi,-pi)
-pi,-pi/6
(-pi/6,5pi/6)
(3pi/2,2pi)
5pi/6,3pi/2
34
(-2pi,-pi)
-pi,-pi/6
(-pi/6,5pi/6)
(3pi/2,2pi)
5pi/6,3pi/2
35
(-2pi,-pi)
-pi,-pi/6
(-pi/6,5pi/6)
(3pi/2,2pi)
5pi/6,3pi/2
36
Table
Graph
37


-2 0 -2

Und. Und. Und.

2 0 2

Graph
Information
38
Table
Information