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Unformatted text preview: † Lecture notes to accompany Section 15.2 of Calculus by HughesHallett et al. 1 Math 10C. Lecture Examples. (11/25/08) Section 15.2, p. 2 Example 5 The function N ( x , y ) = 1 x + 1 y + xy has a minimum for x > , y > . What is it and where does it occur? Answer: The minimum is 3 at (1 , 1). Example 6 What are the values of x and y such that the sum of the squares of the distances from the point ( x , y ) to the four points ( a 1 , b 1 ) , ( a 2 , b 2 ) , ( a 3 , b 3 ) , and ( a 4 , b 4 ) is a minimum? Answer: x = 1 4 ( a 1 + a 2 + a 3 + a 4 ) • y = 1 4 ( b 1 + b 2 + b 3 + b 4 ) (The averages) Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/: ‡ Section 15.1: Examples 1–6 ‡ The chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course....
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 Spring '07
 Hohnhold
 Calculus, Optimization, Web page, Rolle's theorem, 1 dollar

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