Section 3.1 Extra Practice
STUDENT BOOK PAGES 119–129
1. Determine the second derivative for each of the
following functions.
a. g(x) ⫽ ⫺3x 3 ⫹ 6x ⫹ 35
b. h(x) ⫽ (⫺x ⫹ 8) 3
c. y ⫽ x 2 (x ⫹ 5)
d. g(x) ⫽ x(3x ⫺ 4) 3
e. f (x) ⫽ 兹⫺x ⫹ x 2
x2
f. y ⫽
6x ⫹ 4
2. For the following position versus time functions,
determine the functions for velocity and acceleration.
a. s(t) ⫽ ⫺26t 2 ⫺ 4t ⫹ 5
b. s(t) ⫽ t 4 ⫺ 4t 2
t 5 ⫺ 4t 3 ⫹ 6t
c. s(t) ⫽
t2
1
5
d. s(t) ⫽ (t ⫺ 1) 2 ⫹ t 4
2
e. s(t) ⫽ (t 2 ⫹ t) 2
2
⫺1
f. s(t) ⫽ t 3 ⫺ t 2 ⫹ 5
Copyright © 2009 by Nelson Education Ltd.
For questions 3–6, use the given position function
to determine the following.
a. What is the velocity at t ⫽ 10?
b. For t ⱖ 0, when does the direction change?
c. Is there constant acceleration?
3. s(t) ⫽ t ⫹ 5
4. s(t) ⫽ ⫺16t 2 ⫹ 32t ⫹ 5
27
3
5. s(t) ⫽ t 4 ⫺ t 2
4
2
2
6. s(t) ⫽ (t ⫺ 3) 3 ⫹ 3
3
7. For t ⱖ 0, consider the following position versus
time graphs
a.
p(t)
4
3
2
1
0
b.
8
7
6
5
4
3
2
1
0
t
1
2 3 4
p(t)
t
1
2 3 4 5 6
i. When is the velocity zero?
ii. When is the object moving in the positive
direction?
iii. When is the object moving in the negative
direction?
8. Each equation represents the height of an object
projected upward.
1. h(t) ⫽ ⫺5t 2 ⫹ 32t ⫹ 2
2. h(t) ⫽ ⫺5t 2 ⫹ 7t ⫹ 52
3. h(t) ⫽ ⫺5t 2 ⫹ 12t ⫹ 16
a. Which object reached the greatest height?
b. Which object has the greatest velocity as it hits the
ground?
Section 3.1 Extra Practice
357