Analysis and Approaches for IBDP Maths Ebook 1 | Page 157

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Solution
(a) f�
( x)
�
�
2
(2x � x �1)(1) � ( x �1)(4 x �1)
(2x
�x�1)
2 2
2 2
2x � x �1 � (4x � 3x
�1)
(2x
�x�1)
2
�2x
�4x
�
(2x
�x�1)
2 2
2
2x
� 4
x
��
(2x
�x�1)
(b) f�( x) � 0
2 2
2 2
2
2x
� 4
x
�
(2x
�x�1)
2 2
2
2x
4x
0
�0
M1A2
(M1)(A1) for expansion
A1
AG
N0
(M1) for setting equation
� � A1
2 xx� ( 2) � 0
2x � 0 or x �2�
0
x � 0 (Rejected) or x �� 2
(A1) for correct value
f ( � 2)
�2�1
�
(M1)A1 for substitution
2
2( �2) � ( �2) �1
1
��
9
� 1 �
Thus, the coordinates of B are ��2,
� �
� 9 � . A2 N4 [7]
[6]
13
(c) The line y� k does not meet the graph of f
below its minimum point and above its maximum
point.
(R1) for correct argument
1
��1� k � � A2 N3
9
[3]
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