Textbook pdf's

c.
d.
y
6
4
2
–4 –2
0
2
–2
–4
–6
4. a. 0
b. 7
c. 27
d. 3
5. a. x 3 6x x 2
b. x2 2x 3
1x 2 32 2
c. 213x 2 6x216x 62
t 8
d.
1t 42 3 2
6. a.
b.
7. a 2 , 11, 4.52
3 , 2.19b
8. a. If f 1x2 x n , where n is a real
number, then f ¿1x2 nx n1 .
b. If f 1x2 k, where k is a constant,
then f ¿1x2 0.
c. If k1x2 f 1x2g1x2, then
k¿1x2 f ¿1x2g1x2 f 1x2g¿1x2
6
4
2
–6 –4 –2
0
2 4 6
–2
–4
–6
–6 4 6
d. If h1x2 f 1x2 then
g1x2 ,
f ¿1x2g1x2 f 1x2g¿1x2
h¿1x2
3g1x24 2 ,
g1x2 0.
e. If f and g are functions that have
derivatives, then the composite
function h1x2 f 1g1x22 has a
derivative given by
h¿1x2 f ¿1g1x22 # g¿1x2.
f. If u is a function of x, and n is a
positive integer, then
d
dx 1un 2 nu n1du
dx .
y
x 8 28
x 3
x 7 2
x 1
x
x
9. a. As x S ;q, f 1x2 Sq.
b. As x S q, f 1x2 S q.
As x Sq, f 1x2 Sq.
c. As x S q, f 1x2 S q.
As x Sq, f 1x2 S q.
1
10. a. x 0
2x ; 1
b. x 3
x 3 ;
c.
1
no vertical asymptote
1x 42 2 1 ;
1
d. x 3
1x 32 2 ;
11. a. y 0
b. y 4
c. y 1 2
d. y 2
12. a. i. no x-intercept; (0, 5)
ii. (0, 0); (0, 0)
iii. a 5 3 , 0b ; a0, 5 3 b
iv. Q 2 ; no y-intercept
5 , 0R
b. i. Domain: 5xR 0x 16,
Range: 5yR 0y 06
ii. Domain: 5xR 0x 26,
Range: 5yR 0y 46
iii. Domain: e xR 0x 1 ,
2 f
Range: e yR 0y 1 2 f
iv. Domain: 5xR 0x 06,
Range: 5yR 0y 26
12, 1252
Section 4.1, pp. 169–171
1. a. (0, 1), 14, 332
b. (0, 2)
c. a 1 12.25, 48.22,
2 , 0b ,
d. , a1, 5 2 b 2 b
2. A function is increasing when
f ¿1x2 7 0 and is decreasing when
f ¿1x2 6 0.
3. a. i.
ii.
iii.
x 6 1, x 7 2
1 6 x 6 2
11, 42, 12, 12
b. i.
ii.
iii.
1 6 x 6 1
x 6 1, x 7 1
11, 22, (2, 4)
c. i.
ii.
x 6 2
2 6 x 6 2, 2 6 x
iii. none
d. i.
ii.
1 6 x 6 2, 3 6 x
x 6 1, 2 6 x 6 3
iii. (2, 3)
4. a. increasing: x 6 2, x 7 0;
decreasing: 2 6 x 6 0
b. increasing: x 6 0, x 7 4;
decreasing: 0 6 x 6 4
c. increasing: x 6 1, x 7 1;
decreasing: 1 6 x 6 0,
0 6 x 6 1
d. increasing: 1 6 x 6 3;
decreasing: x 6 1, x 7 3
e. increasing: 2 6 x 6 0, x 7 1;
decreasing: x 6 2, 0 6 x 6 1
f. increasing: x 7 0;
decreasing: x 6 0
5. increasing: 3 6 x 6 2, x 7 1;
decreasing: x 6 3, 2 6 x 6 1
6.
y
5
(2, 5)
4
7.
8.
a 3, b 9, c 9
9. a. i.
ii.
iii.
b. i.
ii.
iii.
–2 –1 0
(–1, 0) –1
(–5, 6)
x 6 4
x 7 4
x 4
3
2
1
y
–1
0
1 2 3 4 5
–1
–2
–3
3
2
1
–2
8
4
x 6 1, x 7 1
1 6 x 6 1
x 1, x 1
x
1 2 3 4 5
3
2
1
–3 –2 –1
0
1 2 3
–1
–2
–3
y
–4
0
4
–4
y
(1, 2)
x
x
x
642 Answers
NEL