Solution Manual for Applied CALC, 2nd Edition by Frank Wilson – Complete Chapter 2 Derivatives (Average Rate of Change, Limits, Slope, Algebraic Methods & Interpreting the Derivative)

30 2-1 Average Rate of Change CHAPTER 2 The Derivative 30




Solution Manual Applied CALC 2ND Edition | Frank
Wilson
Exercises 2-1
1.
f (b) g;−f g;(a) g; g;f g;(5) g;−f 5.
= g;
g; g;

q(b) g;−q(a) g; q(6) g;−q(0)
g;(3)
= g;
b g;− g;a 6 g;−0
b g;− g;a 5 g;− g;3 8 g;− 2
5 g;−1 =
= g;
6

2 g ; g ; 2 g;2−
2 = g;
g ;


4 6
= g;
2 g ; 2
= g;
= g;2 6
2.  g;0.2357
v(b)g;−v(a) g; v(1)g;−v(−1)
= g;
b g;− g;a 1− g;(−) 6. average g;rate g;of g;change
−1−(1)
= g; change g;in g;number g;of g;warehouses
2 = g;
−2 g;change g;in g;years
= g;
2 (608 −512)warehouses
= g;
g;

= g;−1 (2012 − 2008) years
g; g; g;

3. = g;24 g;warehouses g;per g;year

v(b) g;−v(a) g; v(4) g;−v(−3)
= g;
b g;− g;a 4g;−g;(−) 7. average g;rate g;of g;change
12 g;−12
= g;
7 change g;in g;number g;of g;Gold g;Star g;members
= g;
0 change g;in g; years
= g;
7
= g;
(24,846 g;−21, g;445)thousands
= g;0 2011− g;2009
= g;1700.5 g;thousand g;members g;per g; year
4.

,31 2-1 Average Rate of Change CHAPTER 2 The Derivative 31

z(b)g−; z(a) g; z(5)g;−z(1) 8. average g;rate g;of g;change
= g;
b g;− g;a 5 g;−1 4
ln(5) g;
ln(5) g; ln(1)
g;
− g; − g;0
= g; g ; g ; 5 1 g ;

,32 2-1 Average Rate of Change CHAPTER 2 The Derivative 32


o arehouse g;change g;in g;number g;of
f
g;warehouses g ;
= g;
(26,736 g;−20,181)thousands
= G 608 g;− g;512

c
o  g;68.28 g;thousand g;Gold g;Star g;members g;per g;warehouse
l
h
d
a
n S
g t
e a
r
i
n m
e
n
u m
m g
;
b b
g
;
e
g
;r
e g
r ;s
/
g
;
w
= g; g ; g ; 5
4
ln(5)
= g;
g;20

 g;0.0805

, 33 2-1 Average Rate of Change CHAPTER 2 The Derivative 33




9. average g;rate g;of g;change 12. g ; f g;(x) g ; = g ; 5

y
change g;in g;Starbucks g;net g;revenue
= g; 7
change g;in g; years 5


(11.7
−9.4)billion g;dollars
3

= g;
g; 1

2011− g; 2007 -1
x
-3
= g;0.575 g;billion g;dollars g;per -5
g; year -7

f (3) g;−f g;(1) g; 5 g;− g;5
= g;
g; g;


10. average g;rate g;of g;change 3g;−1 2
0
= g;
2
number g;o fg;Starbucks g;stores
= g; =g;0
g;change g;in g;years




= g;
(16,858 − g;16, g;680)stores
g;




2010 g;− g;2008 13. f g;(x) g ; = g;(x g;− g;2)2
= g;89 g;stores g;per g;year


11. f g;(x) g ; = g;2x 5
4
y 3
18 2
1
13
0 x
8
-1 0 1 2 3 4

3 -2
x
-2 g; 0
1 2 3 4


f (3) g;−f g;(1) g; 1−1
= g;
-7 g; g;



f (3)g;−f g;(1)g; 8 3g−
; 1 2
= g;
g; g;


g;−2 g;3 g;−1
0
2 = g;
6 2
= g; =g;0
2
= g;3
14.
f (3) g;−f g;(1) g; g;4 g;− g;0
=
g; g;


3g;−1 2
4
= g;
2
=g;2