# Ex 6.5,13 - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at April 15, 2021 by Teachoo

Last updated at April 15, 2021 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 = (๐๐๐๐ ๐ก ๐๐ข๐๐๐๐ ) ร (๐ ๐๐๐๐๐ ๐๐ข๐๐๐๐) = ๐ฅ (24โ๐ฅ) Let P(๐ฅ) = ๐ฅ (24โ๐ฅ) We need product as large as possible Hence we need to find maximum value of P(๐ฅ) Finding Pโ(x) P(๐ฅ)=๐ฅ(24โ๐ฅ) P(๐ฅ)=24๐ฅโ๐ฅ^2 Pโ(๐ฅ)=24โ2๐ฅ Pโ(๐ฅ)=2(12โ๐ฅ) Putting Pโ(๐ฅ)=0 2(12โ๐ฅ)=0 12 โ ๐ฅ = 0 ๐ฅ = 12 Finding Pโโ(๐ฅ) Pโ(๐ฅ)=24โ2๐ฅ Pโโ(๐ฅ) = 0 โ 2 = โ 2 Thus, pโโ(๐ฅ) < 0 for ๐ฅ = 12 ๐ฅ = 12 is point of maxima & P(๐ฅ) is maximum at ๐ฅ = 12 Finding maximum P(x) P(๐ฅ)=๐ฅ(24โ๐ฅ) Putting ๐ฅ = 12 p(12)= 12(24โ12) = 12(12) = 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 (Term 1)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.