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to a zero of its derivative, the number
of zeros of the derivative is the
maximum number of local extreme
values that the function can have. For a
polynomial of degree n, the derivative
has degree n 1, so it has at most
n 1 zeros, and thus at most n 1
local extremes.
3. a. x 3 or x 1
b. no vertical asymptotes
c. x 3
4. a.
y
(1, 37)
30
(3, 21)
15
(5, 5)
–2
0
2 4 6 8 10
–15
–30
x
e.
f.
y
3
2
1
x
–12 –8 –4
0
4 8 12
–1
–2
–3
y
8
6
4
2
–4 –2
0
2 4 6 8 10 12
–2
–4
–6
x
j.
5. a.
b.
y
8
6
4
2
–6 –4 –2
0
2 4 6 8 10
–2
–4
x
b.
60
45
y
(3, 57)
g.
–8
8
y
30
15
( , 30)
2 3
4
–6 –4 –2 0 2 4 6
–4
x
c.
c.
0
–2 2 4 6 8 10
8
4
–4 –2
0
2 4
–4
y
x
x
h.
–8
–12
y
2.0
1.0
–8 –6 –4 –2
0
2 4 6 8
–1.0
x
d.
–8
–2.0
e.
d.
y
(2, 48)
40
(3, 45)
20
–3 –2 –1
0
1 2 3 4
–20
–40
x
i.
y
8
6
4
(3, 3)
2
–8 –6 –4 –2
0
2 4 6 8
–2
–4
(–1, –5)
–6
x
f.
–60
–8
–80
(–2, –80)
NEL
Answers 649