Analysis and Approaches for IBDP Maths Ebook 2 | Page 149

(b) f ( �x) � arcsin( �x) � 4( � x)
A1
(c)
(d)
f ( �x) � �arcsin x � 4x
f ( �x) � �(arcsin x � 4 x)
M1
� f ( �x) � � f ( x)
AG
1
f�( x) � �4(1)
2
1�
x
1
f�( x) � �4
2
1�
x
1 1
� � x �
2 2
0 � x �
4
2 1
(A1) for correct approach
A1
[2]
[2]
11
(e)
3 1 2
x 1
� � � M1
4
3
� � �
2
1 2
1�
�
2
1�
x 3
2
1 x 1
�3 �
1 2
� 4 � � 4 � 0
2
1�
x 3
A1
1 1
�f�( x) � 0 for � � x �
2 2
A1
Thus, there is no local extrema of f( x ) for
1 1
� � x � .
2 2
AG
3
1
�
2 2
f ��( x) � � (1 � x ) ( �2 x) � 0
2
(A1) for correct approach
3
2 2
f ��( x) � x(1 � x )
�
x
f��( x)
�
(1 � x )
3
2 2
A1
[3]
[2]
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