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Ex 6.2, 11 Prove that the function f given by f (๐‘ฅ) = ๐‘ฅ^2 โ€“ ๐‘ฅ + 1 is neither strictly increasing nor strictly decreasing on (โ€“ 1, 1).Given f(๐‘ฅ) = ๐‘ฅ2 โ€“ ๐‘ฅ + 1 Finding fโ€™(๐’™) fโ€™(๐‘ฅ) = 2๐‘ฅ โ€“ 1 Putting fโ€™(๐’™) = 0 2๐‘ฅ โ€“ 1 = 0 2๐‘ฅ = 1 ๐‘ฅ = 1/2 Since ๐’™ โˆˆ (โˆ’๐Ÿ , ๐Ÿ) So, our number line looks like Hence, f(x) is strictly decreasing for ๐‘ฅ โˆˆ (โˆ’1 , 1/2) & f(x) is strictly increasing for ๐‘ฅ โˆˆ (1/2, 1) Hence, f(๐‘ฅ) is neither decreasing nor increasing on (โˆ’๐Ÿ , ๐Ÿ). Hence Proved

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

About the Author

Davneet Singh

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