Differentiation - Problems Involving Maximisation and Minimisation
Differentiation - Problems Involving Maximisation and Minimisation
A man in a boat is \(3\) km from the nearest point of a straight beach. A man is to get to a point \(6\) km along the beach. The man can row at \(4\) km/hr and walk at \(5\) km/hr.
- Show that the time, \(T\) hours, taken to get to his destination is given by \(T = \frac{\sqrt{x^2+9}}{4} + \frac{6-x}{5}, 0 \le x \le 6\).
- Where should the man row to along the beach if he is to reach his destination in the least possible time? What is the least time \(T\)?
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Answer:(a) \(T=\frac{\sqrt{x^2+9}}{4}+\frac{6-x}{5}\), \(0\le x\le 6\) (shown) (b) Row to a point \(4\text{ km}\) from the nearest point on the beach; \(T_{\min}=\frac{33}{20}\text{ h}=1.65\text{ h}\)
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