Transcript Slide 1

Homework, Page 264
Determine the x values that cause the polynomial function to be
(a) zero, (b) positive, and (c) negative.
1. f  x    x  2  x  1 x  5 
 a  f  x   0 for x  2, 1,5
 b  f  x   0 for  2, 1  5,  
 c  f  x   0 for  , 2   1,5 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 1
Homework, Page 264
Determine the x values that cause the polynomial function to be
(a) zero, (b) positive, and (c) negative.


5. f  x   2 x  5  x  8  x  1
2
2
 a  f  x   0 for x  1,8
 b  f  x   0 for  1,8  8,  
 c  f  x   0 for  , 1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 2
Homework, Page 264
Complete the factoring, if needed. Solve the polynomial inequality
using a sign chart. Support graphically.


2
x

1
x
  3x  2  0
9. 
2
 x  1  x  3x  2   0   x  1 x  1 x  2   0
x
1
f  x 
x :  , 1
1

2


1, 2 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 3
Homework, Page 264
Solve the polynomial inequality graphically.
x  x  2x  0
3
13.
2
x  x  2 x  0  x :  1,0
3
2
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
2,  
Slide 2- 4
Homework, Page 264
Solve the polynomial inequality graphically.
17. 3x3  2 x 2  x  6  0
3x3  2 x 2  x  6  0  x :  1.146,  
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 5
Homework, Page 264
Solve the following inequalities for the given function f (x).
a. f  x   0
b. f  x   0
c. f  x   0 d. f  x   0


21. f  x   x 2  4 2 x 2  3

 a  f  x   0,  ,  
 b  f  x   0,  ,  
 c  f  x   0 nowhere
 d  f  x   0 nowhere
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 6
Homework, Page 264
Determine the x-values that cause the function to be:
(a) zero, (b) undefined, (c) positive, and (d) negative.
x 1
25. f  x  
 2 x  3 x  4 
 a  f  x   0,  1.5,1 ,  4,  
 b  f  x   0  1.5,1 ,  4,  
 c  f  x   0  , 1.5  , 1, 4 
 d  f  x   0  , 1.5  , 1,4 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 7
Homework, Page 264
Determine the x-values that cause the function to be:
(a) zero, (b) undefined, (c) positive, and (d) negative.
x5
29. f  x  
 2 x  1 x  1
 a  f  x   0, x  5
 b  f  x  ,  , 5  , x  0.5,1
 c  f  x   0  5, 0.5  1,  
 d  f  x   0  0.5,1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 8
Homework, Page 264
Solve the inequality using a sign chart. Support graphically.
x 1
0
2
x 4
x 1
x 1
0
0
2
x 4
 x  2  x  2 
33.
x
2
1
2
f  x 



x : x  2 or 1  x  2 or x :  , 2    2,  
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 9
Homework, Page 264
Solve the inequality using a sign chart. Support graphically.
37.
x 2  x  12
0
2
x  4x  4
 x  4  x  3
x 2  x  12
0
0
2
x  4x  4
 x  2  x  2 
x
f  x 
4
2

3


x : 4  x  2 or 2  x  3 or x :  4, 2 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
 2,3
Slide 2- 10
Homework, Page 264
Solve the inequality using a sign chart. Support graphically.
x x2 0
41.
x x2  0
x
f  x 
0
2


x : 0  x  2 or x  2 or x :  0, 2 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
 2,  
Slide 2- 11
Homework, Page 264
Solve the inequality.
45.
x3  x  2 
 x  3
x3  x  2 
 x  3
2
x
f  x 
2
0
0
3
0

2


x : 0  x  2 or x :  0, 2 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 12
Homework, Page 264
Solve the inequality.
1
1

0
49.
x 1 x  3
1
1

0
x 1 x  3
x
1
1
3
y 



x : x  1,1  x  3 or x :  , 1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
1,3
Slide 2- 13
Homework, Page 264
Solve the inequality.
53.
 x  5 x  2   0
2x  3
 x  5 x  2 
2x  3
x
f  x
0
1.5
2

5


x :1.5  x  2 or x  5 or x : 1.5, 2 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
5,  
Slide 2- 14
Homework, Page 264
57. Consider the collection of all rectangles that have
length 2 in less than twice their width. Find the possible
widths in inches of these rectangles if their perimeters
are less than 200 in.
l  2w  2  P  2l  2w  200
2  2w  2   2 w  200  4 w  4  2 w  200
6w  204  w  34  1  w  34
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 15
Homework, Page 264
61. Flannery Cannery packs peaches in 0.5-L
cylindrical cans.
A. Express the surface area S of the can as a
function of the radius x (in cm).
500
2
V  500   r h  h  2  S  2 r  2 rh
r
2
500
1000
2
S  2 x  2 x 2  S  2 x 
x
x
2
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Slide 2- 16
Homework, Page 264
61. B. Find the radius and height of the can if the
surface area is 900 cm2.
1000
900  2 x 
 x  1.121,11.368
x
500
500
h
 253.327  h 
 2.463
2
2
 1.121
 11.368 
2
r  1.121cm; h  253.327cm or r  11.368cm; h  2.463cm
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 17
Homework, Page 264
61. C. Find the least possible surface area of the can.
Smin  348.734 cm when x  4.301 cm
2
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 18
Homework, Page 264
65. The graph of f  x   x 4  x  3  x  1 changes
sign at x = 0. Justify your answer.
2
3
False. As shown by the sign chart below, the graph
does not change sign at x = 0.
f  x  x
4
 x  3  x  1
2
3
x
3
0
1
f  x 



Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 19
Homework, Page 264
69. Which of the following is a solution to
A.  ,3 
B.  ,3
C.  ,0  0,3 
D.  ,0   0,3
E. There are no solutions.
2
x
 0?
x 3
x2
 0?
x 3
x
0
f  x 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
3


Slide 2- 20
Homework




Homework Assignment #6
Review Sections 2.1 – 2.8
Page 269, Exercises: 25 – 81 (EOO), 93
Chapter 2 Test next time
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 2- 21