Apps. and Interpretation for IBDP Maths Ebook 1 | Page 381

Answers
58.4 (a) x � 0
(b)
16
f �( x)
� x �
3
x
(c) (2, 4)
(d) �1� x � 0 or x � 2
(e) (i) 8.5
(ii)
15
f �(4)
�
4
(iii)
4
�
15
(iv)
4 287
y� � x�
15 30
(f) y � 4
Exercise 59
59.1 (a) (i)
2
27 � r
h �
2r
(ii) Refer to solution
(b)
dV
27 3 2
� � � �r
dr
2 2
(c) 3 cm
(d)
(i)
3
27�
cm
(ii) 0 �V
� 27�
(e) 1.17 cm and 4.51 cm
59.2 (a) (i) (64 � 2 x)
cm
(b)
(c)
(d)
(e)
(ii) Refer to solution
dV
2
12x
512x
4096
dx � � �
32
x �
3
(i)
3
19418 cm
(ii) 0 �V
� 19418
2
7280 cm
59.3 (a) (i) Refer to solution
(ii) Refer to solution
(b)
dV
25 3 3
r
dr 3 8
(c) r � 6.20
(d)
(e)
3
59.7 cm
1.51�
10 kg/cm
2
�1 3
59.4 (a) (i)
672
h �
2
� r
(ii) Refer to solution
(b)
dA
�1344 � 1
� �r
��
� 336�
2
dr
� � �r
(c) r � 6.24
(d)
(e)
Chapter 16
Exercise 60
60.1
2
184 cm
8 buckets
f x x x x
3 2
( ) � 2 � �8 � 7
60.2 (a)
1 3 3
f ( x) � x �36x
� � 98
3 x
(b) a � 1.5
f( x)
60.3 (a) 1 3 2
� x � 32x �12x
�1008
3
(b) 1008
(c) 3024
60.4 (a)
100 20
f( x) 1
2
x
x
(b) b � 20
Exercise 61
61.1 (a) (i) 10
(ii) (7.67, 50.8)
(b) (i)
3 2
10��x
�16x
�
� � �dx
3
��69x
�90
�
(ii)
2401
12
61.2 (a) (i) � 5
(ii) (5, 0)
(b)
(i)
(ii)
�
0
�5
3 2
�x
� 5x
�
� �dx
��25x
�125�
6875
12
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371