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For all other values of k, the graph will
be similar to the graph below.
12. a. y x 3
b. y 4x 11
13. x 2, x 0, x 2;
increasing: 2 6 x 6 0, x 7 2;
decreasing: x 6 2, 0 6 x 6 2
14. local maximum: 12.107, 17.0542,
local minimum: (1.107, 0.446),
absolute maximum: (3, 24.5),
absolute minimum: 14, 72
15.
y
16. a. p1x2: oblique asymptote, y 0.75x
q1x2: vertical asymptotes at x 1
and x 3; horizontal asymptote at
y 0
r1x2: vertical asymptotes at x 1
and x 1; horizontal asymptote at
y 1
s1x2: vertical asymptote at y 2
b.
–4
–2
4
2
–4 –2
0
2 4
–2
–4
200
150
100
50
–8 –4
0
4 8
–50
–100
–150
–200
10
8
6
4
2
0
–2
–4
y
y
2 4
x
x
x
17. Domain: 5xR 0 x 06;
x-intercept: 2;
y-intercept: 8;
vertical asymptote: x 0; large and
negative to the left of the asymptote,
large and positive to the right of the
asymptote;
no horizontal or oblique asymptote;
increasing: x 7 1.59;
decreasing: x 6 0, 0 6 x 6 1.59;
concave up: x 6 2, x 7 0;
concave down: 2 6 x 6 0;
local minimum at (1.59, 7.56);
point of inflection at 12, 02
–6 –4 –2 0
–4
18. If f 1x2 is increasing, then f ¿1x2 7 0.
From the graph of f ¿, f ¿1x2 7 0 for
x 7 0. If f 1x2 is decreasing, then
f ¿1x2 6 0. From the graph of f ¿,
f ¿1x2 6 0 for x 6 0. At a stationary
point, x 0. From the graph, the zero
for f ¿1x2 occurs at x 0. At x 0,
f ¿1x2 changes from negative to positve,
so f has a local minimum point there.
If the graph of f is concave up, then f –
is positive. From the slope of f ¿, the
graph of f is concave up for
0.6 6 x 6 0.6. If the graph of f is
concave down, then f – is negative.
From the slope of f ¿, the graph of f is
concave down for x 6 0.6 and
x 7 0.6. Graphs will vary slightly.
–2
–1
16
12
8
4
–8
y
19. domain: 5xR 0 x 16;
x-intercept and y-intercept: 10, 02;
vertical asymptote: x 1; large and
positive on either side of the asymptote;
horizontal asymptote: y 0;
increasing: 1 6 x 6 1;
decreasing: x 6 1, x 7 1;
2
1
0
–1
x
2 4 6
y
1 2
x
concave down: x 6 2;
concave up: 2 6 x 6 1, x 7 1;
local minimum at 11, 1.252;
point of inflection: 12, 1.112
–4
–2
20. a. Graph A is f, graph C is f ¿, and
graph B is f –. We know this because
when you take the derivative, the
degree of the denominator increases
by one. Graph A has a squared term
in the denominator, graph C has a
cubic term in the denominator, and
graph B has a term to the power of
four in the denominator.
b. Graph F is f, graph E is f ¿ and graph
D is f –. We know this because the
degree of the denominator increases
by one degree when the derivative is
taken.
Chapter 4 Test, p. 220
1. a. x 6 9 or 6 6 x 6 3 or
0 6 x 6 4 or x 7 8
b. 9 6 x 6 6 or 3 6 x 6 0 or
4 6 x 6 8
c. 19, 12, 16, 22, (0, 1), 18, 22
d. x 3, x 4
e.
f.
f –1x2 7 0
3 6 x 6 0 or 4 6 x 6 8
g. 18, 02, 110, 32
2. a. x 3 or x 1 or x 1 2 2
b. Q 1 local maximum
2 , 17 8 R:
Q 1 local maximum
2 , 15 8 R:
13, 452: local minimum
3.
(–1, 7)
y
6
4 (1, 4)
2
(3, 2)
x
–6 –4 –2
0
2 4 6
–2
–4
–6
6
4
2
0
–2
y
2 4
x
652 Answers
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