Analysis and Approaches for IBDP Maths Ebook 2 | Page 148

Your Practice Set – Analysis and Approaches for IBDP Mathematics
46
Paper 1 Section B – Analysis of Functions
Example
The function f is defined by f ( x) �arcsin x � 4x
, �1� x � 1.
(a) Find f ( � 1) and
f �
�
�
3
2
�
�
.
�
(b) Show that f ( �x) � � f ( x)
for �1� x � 1.
(c) Find f� ( x)
.
(d) Show that there is no local extrema of f( x ) for
(e) Find f�� ( x)
.
1 1
� � x � .
2 2
(f) Find the coordinates of the point of inflexion of f( x ).
(g)
Show that
π
f( x) �4 � for �1� x � 1.
2
[2]
[2]
[2]
[3]
[2]
[4]
[3]
Solution
(a) f ( �1) � arcsin( �1) � 4( � 1)
�
f ( �1) � � � 4
A1
2
3 3 3
f � � arcsin � � 4
� �
� �
�
2 � � 2 � � 2 �
� � � � � �
� 3 � �
f
�
� � 2 3
2 �
� � 3
A1
[2]
138
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