Analysis and Approaches for IBDP Maths Ebook 2 | Page 167

(a) Express CD in terms of x .
(b)
Let H be the total area of the triangles ABP and PCD.
[2]
11
(i) Express H in terms of x .
(ii)
(iii)
Hence, determine the maximum value of H , justifying that this value
is a maximum.
Write down the value of x when H attains its maximum.
[11]
(c)
(d)
Express d � in terms of x .
dx
[3]
Hence, express d H
d� in terms of x . [3]
2. In the figure, ABCD is a parallelogram. It is given that BDC ˆ � 60 , BD �x
� 1 and
CD (6 x)
2
� � , where 1 6
�x
� . Let K be the area of the parallelogram ABCD .
(a) Express K in terms of x .
(b) (i) Express d K
dx in terms of x .
[2]
(ii)
Hence, determine the maximum value of K , justifying that this value
is a maximum.
(iii) Write down the value of x when K attains its maximum.
[8]
(c) Find the range of values of BC .
[4]
(d) Someone claims that BC attains its maximum when K attains its maximum. Do
you agree? Explain your answer.
[3]
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