# Ex 6.5,16 - 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, 16 Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.Let first number be ๐ฅ Now, First number + second number =16 ๐ฅ + second number = 16 second number = 16 โ ๐ฅ Now, Sum of Cubes = (๐๐๐๐ ๐ก ๐๐ข๐๐๐๐ )^3+(๐ ๐๐๐๐๐ ๐๐ข๐๐๐๐ )^3 Let S(๐ฅ) = ๐ฅ3 + (16โ๐ฅ)^3 We Need to Find Minimum Value of s(๐ฅ) Finding Sโ(๐ฅ) Sโ(๐ฅ)= ๐(๐ฅ^3+ (16 โ ๐ฅ)^3 )/๐๐ฅ = 3๐ฅ2 + 3(16โ๐ฅ)^2. (0โ1) = 3๐ฅ2 + 3(16โ๐ฅ)^2 (โ1) = 3๐ฅ2 โ 3((16)^2+(๐ฅ)^2โ2(16)(๐ฅ)) = 3๐ฅ2 โ 3(256+๐ฅ^2โ32๐ฅ) = 3๐ฅ2 โ 3(256)โ3๐ฅ^2+3(32)๐ฅ = โ3(256โ32๐ฅ) Putting Sโ(๐ฅ)=0 โ3(256โ32๐ฅ)=0 256 โ 32๐ฅ = 0 32๐ฅ = 256 ๐ฅ = 256/32 ๐ฅ = 8 Finding Sโโ(๐ฅ) Sโ(๐ฅ)=โ3(256โ32๐ฅ) Sโโ(๐ฅ)=๐(โ3(256 โ 32๐ฅ))/๐๐ฅ = โ3 ๐(256 โ 32๐ฅ)/๐๐ฅ = โ3 [0โ32] = 96 > 0 Since Sโโ(๐ฅ)>0 for ๐ฅ = 8 ๐ฅ = 8 is point of local minima & S(๐ฅ) is minimum at ๐ฅ = 8 Hence, 1st number = x = 8 & 2nd number = 16 โ x = 16 โ 8 = 8

Ex 6.5

Ex 6.5, 1 (i)
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Ex 6.5, 1 (iii) Important

Ex 6.5, 1 (iv)

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Ex 6.5,16 You are here

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Ex 6.5, 27 (MCQ)

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Ex 6.5,29 (MCQ)

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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.