Apps. and Interpretation for IBDP Maths Ebook 1 | Page 379

Answers
Chapter 15
Exercise 53
53.1 (a) f �( x) �12x
�
2
(b)
1
2
(c)
2
23
53.2 (a) f �( x) � 8x
3 1
(b) 2
(c) a �� 2
53.3 (a)
5
f ( �2)
�
2
(b)
1
f �( x)
� x �
2
x
(c) a � 3
53.4 (a) 0
(b)
3 2
f �( x) � x � 1
a
(c) a � 6
Exercise 54
54.1 (a)
54.2 (a)
� � �
3
f ( x) 24x 42x
(b) 108
(c) y�108x�
204
(b)
(c)
54.3 (a)
f �( x) �3�
8x �
1
�
11
1 10
y� � x�
11 11
2
f �( x) �3ax � 4x
(b) a � 4
(c) y�96x�
197
3
54.4 (a)
f �( x) �� 3ax
(b)
1
12a
(c) � 1
(d)
1 67
y� � x�
12 6
Exercise 55
55.1 (a) f �( x) �4x
� 1
(b) g�( x) � 2x
(c)
1
x �
2
(d) 1
55.2 (a)
2
f �( x) �3x � 2x
(b) g�( x) � 1
(c) x �� 1 or
(d)
55.3 (a)
(b)
2
1
x �
3
1
x ��
3
f �( x) �24 � 3x
g�( x) � 3x
(c) x �� 2 or x � 2
(d) 4
55.4 (a) (i) f �( x) �� 2ax
56.1 (a)
(b) a � 1
(c) 1
(d)
9
4
Exercise 56
(ii) g�( x) �� 4
f � x � x � x �
2
2
( ) 6 66 108
(b) 2�x
� 9
56.2 (a)
f�( x)
3 2
� �4x � 60x � 284x
� 420
(b) x � 3 or 5�x
� 7
2
www.seprodstore.com
369