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

3.
V l w h x 2 x 3
x 2 x 3 20
x 3 3x 2 20 0
Possible rational zeros: ±1, ±2, ±4, ±5, ±10, ±20
2 1
x 2
1
3
2
5
or x
0
10
10
x 2x 2 5x 10 0
f x rx
4. False. Since we have qx
dx dx .
f x dxqx rx,
f x f 1
The statement should be corrected to read since qx
x 1 x 1 .
f 1 2
4 1 3a
3 3a
5 ± 15i
2
a 1
b 1 41 5
y x 2 5x 4
20
20
0
(b) Enter the data points
and use the regression feature to obtain
y x2 0, 4, 1, 0, 2, 2, 4, 0,
6, 10
5x 4.
Problem Solving for Chapter 2 259
5. (a)
1, 0: 0 a1
4 a b
4 a 1 4a
2 4, 0: 0 a4
0 16a 4b 4 44a b 1
0 4a b 1 or b 1 4a
b1 4
2 0, 4: 4 a0
4 c
b4 4
2 y ax
b0 c
2 bx c 6. (a)
9 4
Slope 5
3 2
Slope of tangent line is less than 5.
(b)
4 1
Slope 3
2 1
Slope of tangent line is greater than 3.
4.41 4
(c) Slope 4.1
2.1 2
Slope of tangent line is less than 4.1.
f 2 h f 2
(d) Slope
2 h 2
x
x
x + 3
Choosing the real positive value for x we have: x 2
and x 3 5.
The dimensions of the mold are 2 inches 2 inches 5 inches.
(e)
2 h2 4
h
4h h2
h
4 h, h 0
Slope 4 h, h 0
4 1 3
4 1 5
4 0.1 4.1
The results are the same as in (a)–(c).
(f) Letting h get closer and closer to 0, the slope
approaches 4. Hence, the slope at 2, 4 is 4.