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

Ex 6.2, 5 Find the intervals in which the function f given by f (๐‘ฅ) = 2๐‘ฅ3 โ€“ 3๐‘ฅ2 โ€“ 36๐‘ฅ + 7 is (a) strictly increasing (b) strictly decreasingf(๐‘ฅ) = 2๐‘ฅ3 โ€“ 3๐‘ฅ2 โ€“ 36๐‘ฅ + 7 Calculating fโ€™(๐’™) fโ€™(๐‘ฅ) = 6๐‘ฅ2 โ€“ 6๐‘ฅ โ€“ 36 + 0 fโ€™(๐‘ฅ) = 6 (๐‘ฅ2 โ€“ ๐‘ฅ โ€“ 6 ) fโ€™(๐‘ฅ) = 6(๐‘ฅ^2 โ€“ 3๐‘ฅ + 2๐‘ฅ โ€“ 6) fโ€™(๐‘ฅ) = 6(๐‘ฅ(๐‘ฅ โˆ’ 3) + 2 (๐‘ฅ โˆ’ 3)) fโ€™(๐’™) = 6(๐’™ โ€“ 3) (๐’™ + 2) Putting fโ€™(x) = 0 6(๐‘ฅ+2)(๐‘ฅ โ€“3)=0 (๐‘ฅ+2)(๐‘ฅ โ€“3)=0 So, x = โˆ’2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (โˆ’โˆž ,โˆ’๐Ÿ) & (๐Ÿ‘ ,โˆž) f is strictly decreasing in (โˆ’๐Ÿ, ๐Ÿ‘)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.