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Last updated at May 29, 2018 by Teachoo

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Example 34 Find two positive numbers whose sum is 15 and the sum of whose squares is minimum. Let first number be Given sum of two positive number is 15 1st number + 2nd number = 15 + 2nd number = 15 2nd number = 15 Let S be the sum of the squares of the numbers S = (1st number)2 + (2nd number) 2 S = 2 + 15 2 We need to minimize S Finding S S = 2 + 15 2 S = 2 + 15 2 = 2 + 15 2 = 2 + 2 15 1 = 2 2 15 = 2 30+2 = 4 30 Putting S =0 4 30=0 4 =30 = 30 4 = 15 2 Finding S S =4 30 S = 4 30 = 4 Putting = 15 2 in S S 15 2 =4 at = 15 2 s >0 at = 15 2 = 15 2 is local minima Thus, S is Minimum at = 15 2 Hence, 1st number = = 2nd number = 15 =15 15 2 =

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Chapter 6 Class 12 Application of Derivatives

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.