Analysis and Approaches for IBDP Maths Ebook 1 | Page 202

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. Let
3 2
f ( x) � x �9x �15x
� 7 and g( x) � f ( x � 3) . The graph of g is shown below.
The region between x �� 3 and x � 0 is shaded.
(a)
Show that
g x � x � x � .
3
( ) 12 16
(b) Find the coordinates of the point of inflexion of gx. ( )
(c) Hence, write down the coordinates of the point of inflexion of f( x ).
(d)
(e)
4. Let
Find the area of the shaded region.
Hence, write down the value of
3 2
f ( x) 2x 12x 18x
�3
� f ( x )dx
.
�6
� � � � and f ( x) �g( x � 2) . The graph of g is shown below.
[3]
[6]
[2]
[4]
[2]
The region between x �� 2 and x � 0 is shaded.
(a)
Show that
g x � � x � x � .
3
( ) 2 6 4
(b) Find the coordinates of the point of inflexion of gx. ( )
(c)
(d)
Find the area of the shaded region.
Hence, write down the value of
[3]
[6]
[4]
(i)
(ii)
0
2
� f ( x )dx
,
�2
2 � g( x)dx
.
0
[4]
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