Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 5

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Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 6

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Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 7

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

Transcript

Ex 6.2, 6 Find the intervals in which the following functions are strictly increasing or decreasing: (c) โ€“2๐‘ฅ3 โ€“ 9๐‘ฅ2 โ€“ 12๐‘ฅ + 1 f(๐‘ฅ) = โ€“2๐‘ฅ3 โ€“ 9๐‘ฅ2 โ€“ 12๐‘ฅ + 1 Calculating fโ€™(๐’™) fโ€™(๐‘ฅ) = โ€“6๐‘ฅ2 โ€“18๐‘ฅ โ€“ 12 + 0 fโ€™(๐‘ฅ) = โ€“6(๐‘ฅ2+3๐‘ฅ+2) fโ€™(๐‘ฅ) = โ€“6(๐‘ฅ2+2๐‘ฅ+๐‘ฅ+2) fโ€™(๐‘ฅ) = โ€“6(๐‘ฅ(๐‘ฅ+2)+1(๐‘ฅ+2)) fโ€™(๐’™) = โ€“6(๐’™+๐Ÿ) (๐’™+๐Ÿ) Putting fโ€™(๐’™) = 0 โ€“ 6(๐‘ฅ+1) (๐‘ฅ+2) = 0 (๐‘ฅ+1) (๐‘ฅ+2) = 0 So, ๐‘ฅ = โ€“1 , โ€“2 Plotting points on number line Hence, f is strictly increasing for โ€“2 < ๐’™ < โ€“1 & strictly decreasing for ๐’™ < โ€“2 & ๐’™ > โ€“1 Hence, f is strictly increasing for โ€“2 < ๐’™ < โ€“1 & strictly decreasing for ๐’™ < โ€“2 & ๐’™ > โ€“1

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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.