Analysis and Approaches for IBDP Maths Ebook 1 | Page 162

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 53
1. The values of the functions f and g and their derivatives for x � 2 and x � 7 are shown
in the following table.
Let h( x) � f g( x)
.
x f( x ) f� ( x)
gx ( ) g�
( x)
2 30 20 7 � 5
7 10 8 7 2
(a) Find h (2) .
(b) Find h� (7) .
[2]
[3]
2. The values of the functions f and g and their derivatives for x �� 4 and x � 6 are
shown in the following table.
x f( x ) f� ( x)
gx ( ) g�
( x)
� 4 � 3 3 � 1 2
6 5 � 2 6 � 5
Let
f( x)
hx ( ) � .
gx ( )
(a) Find h( � 4) .
(b) Find h� (6) .
3. Let f ( x) � cos�
x , g( x) �ln(3x
� 2) and h( x) � f ( x) � g( x)
. Find h� (1) .
[2]
[3]
[6]
4. Let
f x
2
( ) x 3
� � ,
g( x)
2x
� e and
f( x)
hx ( ) � . Find h� (2) .
gx ( )
[6]
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