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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

Transcript

Ex 6.5, 11 It is given that at ๐‘ฅ = 1, the function ๐‘ฅ4 โ€“ 62๐‘ฅ2 + ๐‘Ž๐‘ฅ+ 9 attains its maximum value, on the interval [0, 2]. Find the value of a. We have f(๐‘ฅ)=๐‘ฅ4 โ€“ 62๐‘ฅ2 + ๐‘Ž๐‘ฅ+ 9 Finding fโ€™(๐’™) fโ€™(๐‘ฅ)=๐‘‘(๐‘ฅ^4โˆ’ 62๐‘ฅ^2 + ๐‘Ž๐‘ฅ + 9)/๐‘‘๐‘ฅ = ใ€–4๐‘ฅใ€—^3โˆ’62 ร—2๐‘ฅ+๐‘Ž = ใ€–4๐‘ฅใ€—^3โˆ’124๐‘ฅ+๐‘Ž Given that at ๐‘ฅ=1, f(๐‘ฅ)=๐‘ฅ^4โˆ’62๐‘ฅ^2+๐‘Ž๐‘ฅ+9 attain its Maximum Value i.e. f(๐‘ฅ) maximum at ๐‘ฅ=1 โˆด ๐‘“โ€™(๐‘ฅ)=0 at ๐‘ฅ=1 Now, fโ€™(1)=0 ใ€–4๐‘ฅใ€—^3โˆ’124๐‘ฅ+๐‘Ž = 0 4(1)^3โˆ’124(1)+a=0 4 โ€“ 124 + a = 0 โ€“120 + a = 0 a = 120 Hence, a = 120

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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.