Analysis and Approaches for IBDP Maths Ebook 1 | Page 173

Front Page
58
Paper 1 Section B – Curve sketching
Example
Consider
f x
2
( ) ln( x 1)
� � � .
14
(a) Find the value of f (0) .
[2]
(b) Find the set of values of x for which f is decreasing.
[5]
(c) Find f�� ( x)
.
[4]
(d) Hence, show that the coordinates of the point of inflexion on the graph of f are
(1, � ln 2) for x � 0 .
[5]
(e) Sketch the graph of f , for x � 0 .
[3]
Solution
(a) f (0)
2
� �ln(0 � 1)
(M1) for substitution
�� ln1
� 0
A1 N2
(b) f�
( x)
1
�� (2 x)
2
x �1
A2
2x
��
2
x �1
f�( x) � 0
R1
2x
� �0
2
x �1
(M1) for valid approach
2x � 0
x � 0
A1 N1
[2]
[5]
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