# Ex 6.5,13 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.5,13 Find two numbers whose sum is 24 and whose product is as large as possible. Let first number be ๐ฅ Now, given that First number + Second number = 24 ๐ฅ + second number = 24 Second number = 24 โ ๐ฅ Product = ๏ท๐๐๐๐ ๐ก ๐๐ข๐๐๐๐ ๏ทฏ ร ๏ท๐ ๐๐๐๐๐ ๐๐ข๐๐๐๐๏ทฏ = ๐ฅ ๏ท24โ๐ฅ๏ทฏ Let P๏ท๐ฅ๏ทฏ = ๐ฅ ๏ท24โ๐ฅ๏ทฏ We need product as large as possible Hence we need to find maximum value of P๏ท๐ฅ๏ทฏ Finding Pโ(x) P๏ท๐ฅ๏ทฏ=๐ฅ๏ท24โ๐ฅ๏ทฏ P๏ท๐ฅ๏ทฏ=24๐ฅโ๏ท๐ฅ๏ทฎ2๏ทฏ Pโ๏ท๐ฅ๏ทฏ=24โ2๐ฅ Pโ๏ท๐ฅ๏ทฏ=2๏ท12โ๐ฅ๏ทฏ Putting Pโ๏ท๐ฅ๏ทฏ=0 2๏ท12โ๐ฅ๏ทฏ=0 12 โ ๐ฅ = 0 ๐ฅ = 12 Finding Pโโ๏ท๐ฅ๏ทฏ Pโ๏ท๐ฅ๏ทฏ=24โ2๐ฅ Pโโ๏ท๐ฅ๏ทฏ = 0 โ 2 = โ 2 Thus, pโโ๏ท๐ฅ๏ทฏ < 0 for ๐ฅ = 12 โ ๐ฅ = 12 is point of maxima & P๏ท๐ฅ๏ทฏ is maximum at ๐ฅ = 12 Finding maximum P(x) P๏ท๐ฅ๏ทฏ=๐ฅ๏ท24โ๐ฅ๏ทฏ Putting ๐ฅ = 12 p๏ท12๏ทฏ= 12๏ท24โ12๏ทฏ = 12๏ท12๏ทฏ = 144 โด First number = x = 12 & Second number = 24 โ x = (24 โ 12)= 12

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Chapter 6 Class 12 Application of Derivatives

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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.