$\"\"$

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The man is in boat $\"\"$ from the nearest point on the coast.

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He is to go to a point $\"\"$ , located $\"\"$ down the coast and $\"\"$ inland.

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$\"\"$

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The man can row at speed of $\"\"$ and walk at $\"\"$ .

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Observe the diagram,

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$\"\"$ and $\"\"$ .

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$\"\"$

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Time $\"\"$ .

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Here the time is considered for both the man can row in water and walking time.

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The time taken by man to reach the point $\"\"$ is $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The man can reach the point $\"\"$ in minimum time when $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The value of $\"\"$ lies between $\"\"$ .

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Graph the function $\"\"$ :

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$\"\"$

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Observe the graph:

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The solution of $\"\"$ is $\"\"$ on $\"\"$ .

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The man should row to a point $\"\"$ from the nearest point on the coast to reach $\"\"$ in minimum time.

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$\"\"$

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The man should row to a point $\"\"$ from the nearest point on the coast to reach $\"\"$ in minimum time.