Analysis and Approaches for IBDP Maths Ebook 1 | Page 207

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4. Let
f ( x)
3
� . The following diagram shows part of the graph of f .
x
The point A( h, f ( h )) , where h � 0 , lies on the graph of f . The normal at A crosses the
x -axis at the point B( b , 0) .
16
(a) (i) Show that the equation of [AB] is
4
1 3h
�1
x
2
3h
3h
y� � � .
(b)
(ii) Find b in terms of h .
[9]
Show that the area between the graph of f , the normal at A and the x -axis is
1 4 4
(6 1)
4 h h � . [6]
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