Analysis and Approaches for IBDP Maths Ebook 1 | Page 195

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3. The graph of a function f has a local minimum point at A , where x � 0 . The derivative
of f is given by
origin.
f � x �x
� . It is also given that the graph of f passes through the
2
( ) 9
(a) Find an expression for f( x ).
[6]
(b) Find the coordinates of A .
[6]
The graph of a function g is obtained by vertically stretching the graph of f with scale
�1
�
factor 2, followed by a translation of � �.
�4�
15
(c) Find the coordinates of the image of A .
[4]
4. The graph of a function f has a local maximum point at A , where x � 0 . The derivative
of f is given by f �( x) � �2( x � 2) . It is also given that the graph of f passes through
(1, � 5) .
(a) Find an expression for f( x ).
(b) Find the coordinates of A .
The graph of a function g is obtained by horizontally stretching the graph of f with
[6]
[4]
scale factor 1 , followed by a reflection of the graph of f in the x -axis.
3
(c) Find the coordinates of the image of A .
[4]
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