Analysis and Approaches for IBDP Maths Ebook 1 | Página 169

(d) f�( x) � 0
2
3(2) x 2( 27) x 4( 27) 0
� � � � � (M1) for setting equation
2
6x
�54x�108 � 0
2
x �9x�18 � 0
( x�3)( x�6) � 0
x � 3 or x � 6 (Rejected) A1
f (3)
3 2
� 2(3) � ( �27)(3) � 4( �27)(3) �( � 27)
� 162
Thus, the coordinates are (3,162). A2 N3
[4]
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13
Exercise 56
3 2
1. Let f ( x) � ax �bx �8bx � a , where a and b are real numbers. The graph of f passes
through the point ( � 2, 29) .
(a) Show that 7a�12b� � 29 .
The graph of f has a local maximum at ( � 2, 29) .
[2]
(b) Find the other equation in a and b , giving your answer in a similar form to part
(a).
[5]
(c) Find the value of a and of b .
[3]
(d) Find the coordinates of the local minimum point of the graph of f .
[4]
3
2. Let f ( x)
� ax �bx � b , where a and b are real numbers. The graph of f passes
through the point ( � 5, 350) .
(a) Show that 125a� 4b� � 350 .
The graph of f has a local maximum at ( � 5, 350) .
[2]
(b) Find the other equation in a and b , giving your answer in a similar form to part
(a).
[5]
(c) Find the value of a and of b .
[3]
(d) Find the coordinates of the local maximum point of the graph of f .
[4]
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