Analysis and Approaches for IBDP Maths Ebook 1 | Page 159

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The graph of f has a local minimum at
� 2 �
A��6,
� �
� 3 �
and a local maximum at B .
(a)
Use the quotient rule to show that
(b) Hence find the coordinates of B .
f�( x)
��
2
6( x �8x�12)
( x � 3 x)
2 2
(c) Given that the line y� k meets the graph of f , find the possible values of k .
.
[6]
[7]
[3]
13
3. Let
1
f( x) � �2
�� x �
cos�
�
� 2 �
for �1� x � 3, x � 1. The graph of f is given below.
The graph of f has a local minimum at P(0, 3) and a local maximum at Q .
(a)
Use the quotient rule to show that
(b) Hence find the coordinates of Q .
��
x �
� sin � �
2
f�( x)
�
� �
.
2 ��
x �
2cos � �
� 2 �
(c) Given that the line y� k meets the graph of f at two distinct points, find the
possible values of k .
[5]
[7]
[3]
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