Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12
Ex 6.2,14 - Chapter 6 Class 12 Application of Derivatives
Last updated at Jan. 7, 2020 by Teachoo
Transcript
Ex 6.2, 14 Find the least value of a such that the function f given by ๐ (๐ฅ) = ๐ฅ2 + ๐๐ฅ + 1 is strictly increasing on (1, 2). We have f(๐ฅ) = ๐ฅ2 + a๐ฅ + 1 And, fโ(๐ฅ) = ๐ฅ2 + a๐ฅ + 1 fโ(๐ฅ) = 2๐ฅ + a. Given f is strictly increasing on (1 ,2) โด fโ(๐ฅ) > 0 on (1 ,2) Thus, 2๐ฅ + a > 0 on (1 ,2) Putting ๐ = 1 2(1) + a > 0 2 + a > 0 a > โ2 Putting ๐ = 2 2(2) + a > 0 4 + a > 0 a > โ4 โด When a > โ2 , f(๐ฅ) = ๐ฅ2 + a๐ฅ + 1 is strictly increasing on (๐ , ๐) Hence, least value of a is โ2
Chapter 6 Class 12 Application of Derivatives
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