Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

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

Transcript

Example 10 Find the intervals in which the function f given by f (x) = x2 โ€“ 4x + 6 is (a) strictly increasing (b) strictly decreasing f (๐‘ฅ) = ๐‘ฅ2 โ€“ 4๐‘ฅ + 6 Calculate fโ€™(๐’™) ๐‘“โ€™ (๐‘ฅ) = 2๐‘ฅ โ€“ 4 Calculate fโ€™(๐’™) = 0 2๐‘ฅ โ€“ 4 = 0 2๐‘ฅ = 4 ๐‘ฅ = 4/2=2 Hence ๐‘ฅ = 2 divide real line into 2 disjoint intervals. Plotting points on number line fโ€™(x) = 2x โˆ’ 4 For x < 2, fโ€™(x) is negative i.e. fโ€™(๐‘ฅ) < 0 Hence f is strictly decreasing in interval (โˆ’ โˆž ,๐Ÿ) fโ€™(๐‘ฅ) = 2๐‘ฅ โˆ’ 4 For x > 2, fโ€™(๐‘ฅ) is positive i.e. fโ€™(๐‘ฅ) > 0 Hence, f is strictly increasing in interval (2 , โˆž)

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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.