Analysis and Approaches for IBDP Maths Ebook 1 | Page 206

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(a) (i) Find two different expressions of f� ( a)
.
(ii) Hence show that a � 2 .
(b)
3. Let
f ( x)
(iii) Find the equation of [PQ] in the form y �mx � c .
Find the area between the graph of f , the tangent at P and the x -axis.
1
2
� x . The following diagram shows part of the graph of f .
[8]
[6]
The point A( h, f ( h )) , where h � 0 , lies on the graph of f . The tangent at A crosses the
x -axis at the point B( b , 0) .
(a) (i) Show that the equation of [AB] is
y 1 1
�
2
x �
h 2
h .
(b)
(ii) Find b in terms of h .
[7]
Show that the area between the graph of f , the tangent at A and the x -axis is
1
3 h h. [6]
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