Apps. and Interpretation for IBDP Maths Ebook 1 | Page 217

60
Paper 1 – Finding the Original Functions
Example
The derivative of f is given by
(0, � 3) . Find an expression for f( x ).
2
f �( x) � 3x �3x
� 18. The y -intercept of the graph is at
[5]
Solution
16
� (M1) for indefinite integral
2
f ( x) � (3x � 3x �18)dx
3 2
� � � �
x x
f ( x) � 3� � � 3� � �18x � C
(A2) for correct integration
� 3 � � 2 �
3 3 2
f ( x) � x � x �18x � C
2
3 3 2
�3 � 0 � (0) �18(0)
� C
(M1) for substitution
2
C �� 3
3
2
3 2
� f ( x) � x � x �18x
� 3
A1 N5
[5]
Exercise 60
1. The derivative of f is given by
(0, 7) . Find an expression for f( x ).
f � x � x � x � . The y -intercept of the graph is at
2
( ) 6 2 8
[5]
2. The derivative of f is given by
the graph is at (3, 0).
2 3
f �( x) � x �36
� , where x � 0 . The x -intercept of
2
x
(a) Find an expression for f( x ).
(b)
The graph of f passes through
� 377 �
�a,
�
� 8 � , where 0 � a � 4 . Find the value of a .
[5]
[2]
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