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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 decreasing f(๐‘ฅ) = 2๐‘ฅ3 โ€“ 3๐‘ฅ2 โ€“ 36๐‘ฅ + 7 Calculating fโ€™(๐’™) f (๐‘ฅ) = 2๐‘ฅ3 โ€“ 3๐‘ฅ2 โ€“ 36๐‘ฅ + 7 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‘ฅ) = 6(๐‘ฅ โ€“ 3) (๐‘ฅ + 2) Putting fโ€™(๐’™) = 0 6(๐‘ฅ + 2) )(๐‘ฅ โ€“ 3) = 0 (๐‘ฅ + 2) (๐‘ฅ โ€“ 3) = 0/6 (๐‘ฅ + 2) (๐‘ฅ โ€“ 3) = 0 So, x = โ€“ 2 & x = 3 Plotting points on real line โˆด Points โ€“2 , & 3 divide the real line into 3 disjoint intervals i.e. ( โ€“ โˆž , โˆ’2) ( โ€“2 , 3) & (3 , โˆž) Thus, (a) f is strictly increasing in ( โ€“โˆž , โ€“2) & (3 , โˆž) (b) f is strictly decreasing in ( โ€“2 , 3)

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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.