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

Transcript

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). Let f(๐‘ฅ) = ๐‘ฅ2 โ€“ ๐‘ฅ + 1 ๐‘ฅ โˆˆ (โˆ’1 , 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‘ฅ โˆˆ (โˆ’1 , 1), So, our number line looks like The point ๐‘ฅ = 1/2 divide the intervals (โˆ’1 , 1) into two disjoint intervals. i.e. (โˆ’1 , 1/2) & (1/2 , 1) 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

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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.