Analysis and Approaches for IBDP Maths Ebook 1 | Page 203

Front Page
69
Paper 1 Section B – Areas between
curves, tangents and normals
Example
Let
f ( x)
3
� . The following diagram shows part of the graph of f .
x
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
(a) (i) Find f� ( a)
.
(ii) Hence show that a � 1.
(iii) Find b .
1
� .
3
(b)
(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.
[8]
[6]
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