Differentiation - Problems Involving Maximisation and Minimisation
Differentiation - Problems Involving Maximisation and Minimisation
TGM Original Questions
As shown in the diagram, a person in a boat is \(3\) km from the nearest point from the straight beach. The person is to get to a cabin \(6\) km along the beach. It is known that the boat travels at \(4\) km/h and the person walks at \(5\) km/h. Assume that the person lands at a point \(x\) km from the point directly opposite to the original position.
- Find, in terms of \(x\), the total time (in hours) taken for the person to reach the cabin.
- Find the value of \(x\) for which the total time taken is the minimum and find this minimum time.
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Answer:(i) \(T=\dfrac{\sqrt{x^2+9}}{4}+\dfrac{6-x}{5}\text{ h}\) (ii) \(x=4\text{ km}\), minimum time \(=\dfrac{33}{20}\text{ h}=1.65\text{ h}\)
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