C H A P T E R 2 Polynomial and Rational Functions

256 Chapter 2 Polynomial and Rational Functions
137. (a)
y
2 in. 2 in.
(b) The area of print is x 4y 4, which is
30 square inches.
0
0
x 4y 4 30
x
2 in.
2 in.
y 4 30
x 4
y 30
4
x 4
y
y
y
30 4x 4
x 4
4x 14
x 4
22x 7
x 4
22x 7 2x2x 7
Total area xy x x 4
x 4
100
(c) Because the horizontal margins total 4 inches, x must be
greater than 4 inches. The domain is x > 4.
(d)
200
4 32
0
The minimum area occurs when x 9.477 inches, so
y
22 9.477 7
9.477 4
9.477 inches.
The least amount of paper used is for a page size of about
9.48 inches by 9.48 inches.
138.
The limiting amount of uptake is determined
by the horizontal asymptote,
y
90
18.47
0.23 80.3 mgdm2 18.47x 2.96
y , 0 < x
0.23x 1
139.
CO2 hr.
Critical numbers:
Test intervals: ,
Test: Is 3x 42x 1 < 0?
4
x
3 , , 43
4
6x
3x 42x 1 < 0
1
3 , x 2
2 6x
5x 4 < 0
2 5x < 4
140.
2 x 2 x ≥ 15 141.
2 x 2 x 15 ≥ 0
Critical numbers: x
Test intervals: , 3 ⇒ 2x 5x 3 > 0
5
2x 5x 3 ≥ 0
2 , x 3
5 2 , 3,
⇒ 2x 5x 3 > 0
5
2 ⇒ 2x 5x 3 < 0
Solution interval: , 3 5
2 ,
1
, 2, 1 2 ,
By testing an x-value in each test interval in the
inequality, we see that the solution set is: 4
3
x 3 16x ≥ 0
xx 4x 4 ≥ 0
Critical numbers:
Test intervals:
x 0, x ±4
Test: Is xx 4x 4 ≥ 0?
By testing an x- value in each test interval in the inequality,
we see that the solution set is: 4, 0 4, .
, 1
2
, 4, 4, 0, 0, 4, 4,