Explanation Given: A boat moves north at a constant speed. A second boat, moving at the same speed, pursues the first boat in such a way that it always points directly at the first boat. When the first boat reaches the point ( 0 , 1 ) , the second boat is at the point ( 6 , 2.5 ) , with the positive y − axis pointing north. It can then be shown that the curve traced by the second boat, known as a pursuit curve, is given by y = x 2 16 − 2 ln x + 1 4 + 2 ln 6 . Approach: To find the absolute extrema (maximum/minimum) for a function f on a closed interval [ a , b ] : Find critical points of f in ( a , b ) by solving f ′ = 0 . Evaluate f for all the critical points. The largest value is the maximum and the smallest value is the minimum. For a function y = f ( x ) whose derivative exists, the differential of x , written d x , is an arbitrary real number (usually small compared with x ); the differential of y written as d y , is the product of f ′ ( x ) and d x . For small nonzero values of Δ x , d y ≈ Δ y , and, f ( x + Δ x ) ≈ f ( x ) + d y = f ( x ) + f ′ ( x ) d x

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 6.CR, Problem 61CR

To determine

To find:

The y− coordinate of the southernmost point of second boat’s path.

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Chapter 6.CR, Problem 60CR

Chapter 6.CR, Problem 62CR

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