Ex 6.2,15 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 6.2, 15 Let I be any interval disjoint from [โ1, 1]. Prove that the function f given by ๐(๐ฅ) = ๐ฅ + 1/๐ฅ is strictly increasing on I.I is any interval disjoint from [โ1, 1] Let I = (โโ, โ๐)โช(๐, โ) Given f(๐ฅ) = ๐ฅ + 1/๐ฅ We need to show f(๐ฅ) is strictly increasing on I i.e. we need to show fโ(๐) > 0 for ๐ฅ โ (โโ, โ๐)โช(๐, โ) Finding fโ(๐) f(๐ฅ) = ๐ฅ + 1/๐ฅ fโ(๐ฅ) = 1 โ 1/๐ฅ2 fโ(๐ฅ) = (๐ฅ2 โ 1)/๐ฅ2 Putting fโ(๐) = 0 (๐ฅ2 โ 1)/๐ฅ2 = 0 ๐ฅ2โ1 = 0 (๐ฅโ1)(๐ฅ+1)=0 So, ๐=๐ & ๐=โ๐ Plotting points on number line The point ๐ฅ = โ1 , 1 into three disjoint intervals โด f(x) is strictly increasing on (โโ , โ๐) & (๐ , โ) Hence proved
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo