Analysis and Approaches for IBDP Maths Ebook 1 | Page 163

54
Example
Paper 2 Section A – Binomial expansion on derivatives
Front Page
13
Let
f ( x) ( 5)
2 6
� x � . Find the term in
� .
3
x in the expansion of the derivative, f ( x)
[7]
Solution
f�
( x)
� �
2 5
6( x 5) (2 x)
2 5
�12 xx ( � 5)
A2
The ( r �1)
th term
��5�
�
2 5�r
r
�12 x�� �( x ) ( �5)
�
M1
��r
�
�
�5�
11 2
12 ( 5) r �
� � � � x
r
�r
�
�11 � 2r
� 3
R1
�2r
� � 8
r � 4
(A1) for correct value
3
The term in x
�5�
4 11 2(4)
�12 � �( �5)
x �
(A1) for correct expansion
�4�
3
� 37500x
A1 N3
[7]
Exercise 54
1. Let
f ( x) (1 2 )
2 5
� � x . Find the term in
� .
7
x in the expansion of the derivative, f ( x)
[7]
2. Let
f ( x) (4 7)
3 8
� x � . Find the term in
� .
11
x in the expansion of the derivative, f ( x)
[7]
3. Let
g( x) ( x 2 x)
2 5
� � . Find the term in
� .
6
x in the expansion of the derivative, g ( x)
[7]
4. Let
4
� 1 �
g( x) ��2x
� �
� x � . Find the term in 3
x � in the expansion of the derivative, g� ( x)
.
[7]
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