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Tuition Center Singapore JC Math Tuition – Differentiation and Applications
Tuition Center Singapore JC Math Tuition – Differentiation and Applications
ABCD is a rectangular field whose sides, AB and BC, measure 2a m and a m respectively. A road runs along the side AB. A man, starting from A, wishes to reach the opposite corner C in the shortest possible time. He can walk along the road at 100 m per minute and across the field at 60 m per minute.
Find an expression for the time, in minutes, he will take if he walks along the road to P, a point x m from B, and then across the field from P to C.
Use differentiation to find, in terms of a, the value of x for the time taken to be the shortest possible. Find, also, the shortest possible time taken, and prove that it is the minimum.
Answer
T = (2a- x )/100 + sq rt (x^2 = a^2)/60
min T = a/30 min
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