Analysis and Approaches for IBDP Maths Ebook 1 | Page 161

Front Page
53
Example
Paper 2 Section A – Rules of differentiation
13
The values of the functions f and g and their derivatives for x � 3 and x � 5 are shown
in the following table.
x f( x ) f� ( x)
gx ( ) g�
( x)
3 10 14 3 � 12
5 8 20 � 9 7
Let h( x) � f ( x) g( x)
.
(a) Find h (5) .
(b) Find h� (3) .
[2]
[3]
Solution
(a) h (5)
� f(5) g(5)
(A1) for valid approach
�(8)( � 9)
�� 72
A1 N2
(b) h� (3)
� f �(3) g(3) � f (3) g�(3)
(M1) for product rule
� (14)(3) � (10)( � 12)
(A1) for substitution
�� 78
A1 N2
[2]
[3]
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