Analysis and Approaches for IBDP Maths Ebook 1 | Page 176

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. Consider
f ( x)
� e �kx , k � 0 .
2
(a) Find the value of f (0) .
(b) Find f� ( x)
and f�� ( x)
in terms of k .
The graph of f has a point of inflexion when x �� 1 for x � 0 .
(c) Find the value of k .
(d)
Show that the coordinates of the point of inflexion on the graph of f are
� 1 �
��1,
�
� e � for x � 0 .
(e) Show that f is non-decreasing for x � 0 .
(f) Sketch the graph of f , for x � 0 .
[2]
[5]
[2]
[1]
[3]
[3]
kx
4. Consider f( x)
��
2
( x �1)
for x �� 1, k � 0 .
(a) Find the x -intercept of the graph of f .
(b) Find f� ( x)
and f�� ( x)
in terms of k .
The graph of f has no maximum point and the coordinates of the minimum point on
graph of f are (1, � 1) .
(c) Find the value of k .
(d)
Show that the coordinates of the point of inflexion on the graph of f are
� 8 �
�2,
� �
� 9 � for x �� 1.
(e) Sketch the graph of f , for x �� 1.
[2]
[6]
[2]
[5]
[3]
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