Analysis and Approaches for IBDP Maths Ebook 2 | Page 168

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. In the figure, ABCD is a rectangular farm with length 500 m and width 250 m. Sam is at
A and plans a route to C . He first walks across the farm by x m to reach P , where P is
a point on CD . Then he runs towards C along CD . His running speed is 4 metres per
second, and his walking speed in the farm is half of that when he is travelling along CD .
Let T be his total travelling time.
(a) Express T in terms of x .
(b) (i) Express d T
dx in terms of x .
[3]
(ii)
Hence, determine the minimum value of T , justifying that this value
is a minimum.
(iii)
Write down the value of x when T attains its minimum.
Let L be his total distance travelled.
[9]
(c)
(d)
Show that
dL
�1�
x
dx
2
x � 62500
.
Someone claims that d L
is increasing when T attains its minimum. Do
dx you agree? Explain your answer.
[2]
[3]
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