Ex 6.2, 6 (c) - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 6.2, 6 Find the intervals in which the following functions are strictly increasing or decreasing: (c) โ2๐ฅ3 โ 9๐ฅ2 โ 12๐ฅ + 1 f(๐ฅ) = โ2๐ฅ3 โ 9๐ฅ2 โ 12๐ฅ + 1 Calculating fโ(๐) fโ(๐ฅ) = โ6๐ฅ2 โ18๐ฅ โ 12 + 0 fโ(๐ฅ) = โ6(๐ฅ2+3๐ฅ+2) fโ(๐ฅ) = โ6(๐ฅ2+2๐ฅ+๐ฅ+2) fโ(๐ฅ) = โ6(๐ฅ(๐ฅ+2)+1(๐ฅ+2)) fโ(๐) = โ6(๐+๐) (๐+๐) Putting fโ(๐) = 0 โ 6(๐ฅ+1) (๐ฅ+2) = 0 (๐ฅ+1) (๐ฅ+2) = 0 So, ๐ฅ = โ1 , โ2 Plotting points on number line Hence, f is strictly increasing for โ2 < ๐ < โ1 & strictly decreasing for ๐ < โ2 & ๐ > โ1 Hence, f is strictly increasing for โ2 < ๐ < โ1 & strictly decreasing for ๐ < โ2 & ๐ > โ1
Ex 6.2
Ex 6.2,2
Ex 6.2,3 Important
Ex 6.2,4
Ex 6.2, 5 Important
Ex 6.2, 6 (a)
Ex 6.2, 6 (b) Important
Ex 6.2, 6 (c) Important You are here
Ex 6.2, 6 (d)
Ex 6.2, 6 (e) Important
Ex 6.2, 7
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Ex 6.2,9 Important
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Ex 6.2, 12 (A)
Ex 6.2, 12 (B) Important
Ex 6.2, 12 (C) Important
Ex 6.2, 12 (D)
Ex 6.2, 13 (MCQ) Important
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Ex 6.2,19 (MCQ) Important
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo