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

Transcript

Ex 6.2, 14 Find the least value of a such that the function f given by ๐‘“ (๐‘ฅ) = ๐‘ฅ2 + ๐‘Ž๐‘ฅ + 1 is strictly increasing on (1, 2). We have f(๐‘ฅ) = ๐‘ฅ2 + a๐‘ฅ + 1 And, fโ€™(๐‘ฅ) = ๐‘ฅ2 + a๐‘ฅ + 1 fโ€™(๐‘ฅ) = 2๐‘ฅ + a. Given f is strictly increasing on (1 ,2) โˆด fโ€™(๐‘ฅ) > 0 on (1 ,2) Thus, 2๐‘ฅ + a > 0 on (1 ,2) Putting ๐’™ = 1 2(1) + a > 0 2 + a > 0 a > โ€“2 Putting ๐’™ = 2 2(2) + a > 0 4 + a > 0 a > โ€“4 โˆด When a > โ€“2 , f(๐‘ฅ) = ๐‘ฅ2 + a๐‘ฅ + 1 is strictly increasing on (๐Ÿ , ๐Ÿ) Hence, least value of a is โ€“2

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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.