Analysis and Approaches for IBDP Maths Ebook 1 | Page 201

Front Page
Exercise 68
1. Let
1 2
f ( x) � ( x � a)
, �6� x � 6, a� . The graph of f is shown below.
4
2. Let
The region between x � 2 and x � 4 is shaded.
(a) Show that f ( �x) � f ( x)
.
[2]
(b) Given that the coordinates of the minimum point are (2 � aa , ) , show that a � 2 .
[3]
(c) Show that there is no point of inflexion.
[2]
(d) Find the area of the shaded region.
[4]
�2
(e) Hence, write down the value of � f ( x )dx
.
3
ax
f( x)
�
4
x � 1
, � 8 � x � 8 , a� . The graph of f is shown below.
�4
[2]
16
The region between x � 1 and x � 2 is shaded.
(a) Show that f ( �x) � � f ( x)
.
[2]
2 4
ax (3 � x )
(b) Given that f�( x)
� , find the coordinates of the maximum point and
4 2
( x �1)
the minimum point in terms of a .
[6]
(c) Find the area of the shaded region, giving your answer in terms of a and in the
form pln
q.
[6]
1
(d) Hence, write down the value of f ( x
2 a
� )dx
if ( )d ln17
0 � f x x � .
0
4
[2]
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