Analysis and Approaches for IBDP Maths Ebook 1 | Page 205

Front Page
Exercise 69
1. Let
f ( x)
1
2
� x . The following diagram shows part of the graph of f .
16
The point P( a, f ( a )) , where a � 0 , lies on the graph of f . The normal at P crosses the
x -axis at the point Q( b , 0) .
It is given that the gradient of [PQ] is � 4 .
(a) (i) Find f� ( a)
.
(ii) Hence show that a � 4 .
(iii) Find b .
(b)
2. Let
f ( x)
(iv) Find the equation of [PQ] in the form y �mx � c .
Find the area between the graph of f , the normal at P and the x -axis.
2
� . The following diagram shows part of the graph of f .
x
[8]
[6]
The point P( a, f ( a )) , where a � 0 , lies on the graph of f . The tangent at P crosses the
x -axis at the point Q(1, 0) .
www.seprodstore.com
197