Analysis and Approaches for IBDP Maths Ebook 1 | Page 194

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(c) g( x) � � f ( x �7) � 11
(A1) for transformation
The local minimum point on the graph of g is the
image of A .
(M1) for recognizing image
The x -coordinate of the required point
� �3�
7
� 4
A1 N3
[3]
Exercise 66
1. The graph of a function f has a local minimum point at A , where x � 0 . The derivative
of f is given by
f � x � x � x � .
2
( ) 3 2 8
(a) Find the x -coordinate of A .
(b) The y -intercept of the graph is at (0, 7) . Find an expression for f( x ).
The graph of a function g is obtained by reflecting the graph of f in the x -axis,
��3�
followed by a translation of � �.
��4�
(c) Find the x -coordinate of the local maximum point on the graph of g .
[5]
[6]
[4]
2. The graph of a function f has a local maximum point at A , where x � 0 . The derivative
of f is given by
2
� � � .
f ( x) 36 x
(a) Find the x -coordinate of A .
(b) The y -intercept of the graph is at (0, 6) . Find an expression for f( x ).
The graph of a function g is obtained by reflecting the graph of f in the y -axis,
�6�
followed by a translation of � �.
�5�
(c) Find the x -coordinate of the local maximum point on the graph of g .
[5]
[6]
[4]
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