Analysis and Approaches for IBDP Maths Ebook 1 | страница 170

Your Practice Set – Analysis and Approaches for IBDP Mathematics
2
3. Let ( ) x x
g x � ae �be � 126x
, where a and b are real numbers, for 0�x
� 4. The graph
of g passes through the point (ln 5, �225 � 126ln 5) .
(a) Show that 5a� b� � 45 .
The graph of g has a point of inflexion at (ln5, �225 � 126ln5) .
[3]
4. Let
(b) Find the other equation in a and b , giving your answer in a similar form to part
(a).
[6]
(c) Find the value of a and of b .
[3]
(d) Find the horizontal distance between the two stationary points of the graph of g
for 0�x
� 4.
[4]
2
( ) x x
g x ae be 100x
� � � , where a and b are real numbers, for 0�x
� 5. The graph
of g passes through the point
� 15 675 15 �
�ln , � �100ln
�
� 2 4 2 � .
(a) Show that 225a� 30b� 675 � 0 .
The graph of g has a point of inflexion at
� 15 675 15 �
�ln , � �100ln
�
� 2 4 2 � .
[3]
(b) Find the other equation in a and b , giving your answer in a similar form to part
(a).
[6]
(c) Find the value of a and of b .
[3]
(d) Find the coordinates of the local maximum point of the graph of g .
[6]
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