Analysis and Approaches for IBDP Maths Ebook 1 | Page 178

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(c) S�
( �)
�0 � (cos2 �)(2)
(M1) for differentiation
�� 2cos2�
S�( �) � 0
(M1) for setting equation
�2cos 2�
� 0
cos2� � 0
�
2� �
2
�
� �
4
A1 N3
By the first derivative test,
M1A1
�
� � �
� � � � � �
4 4 4
S� ( �)
� 0 �
�
Thus, S attains its minimum at � � .
4
R1 N0
(d) S is greatest when sin 2� is smallest. R1
�
��
� 0 or � � A1 N2
2
[6]
[2]
Exercise 59
1. The following diagram shows a semicircle with centre O , diameter AB and radius 4. Let
C be a point on the circumference with BOC ˆ � � radians, where 0 �� � � . Let P be
the area of the triangle ABC .
(a) Show that P � 16sin�
.
[4]
(b) Find the value of � when P is a local maximum, justifying that it is a maximum.
[6]
(c) Find the maximum value of P .
[2]
(d) Write down the values of � for which P has its least value.
[2]
170
SE Production Limited