Ex 6.2, 3 - Find the intervals in which f(x) = sin x - Ex 6.2

Ex 6.2,3 - Chapter 6 Class 12 Application of Derivatives - Part 2

Ex 6.2,3 - Chapter 6 Class 12 Application of Derivatives - Part 3

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

Transcript

Ex 6.2, 3 Find the intervals in which the function f given by f (๐‘ฅ) = sin ๐‘ฅ is (a) strictly increasing in (0 , ๐œ‹/2) f(๐‘ฅ) = sin ๐‘ฅ fโ€™(๐’™) = cos ๐’™ Since cos ๐‘ฅ > 0 for ๐‘ฅ โˆˆ ("0 , " ๐œ‹/2) โˆด fโ€™(๐‘ฅ) < 0 for ๐‘ฅ โˆˆ (0 , ฯ€) Thus, f is strictly increasing in ("0 , " ๐œ‹/2) Rough cos 0 = 1 cos ๐œ‹/4 = 1/โˆš2 cos ๐œ‹/2 = 0 Value of cosโก๐‘ฅ > 0 for (0 , ๐œ‹/2) Ex 6.2, 3 Find the intervals in which the function f given by f (๐‘ฅ) = Sin x is (b) strictly decreasing (๐œ‹/2,๐œ‹)f(๐‘ฅ) = sin ๐‘ฅ fโ€™(๐’™) = cos ๐’™ Since cos ๐‘ฅ < 0 for ๐‘ฅ โˆˆ (๐œ‹/2 , ๐œ‹) โˆด fโ€™(๐‘ฅ) < 0 for ๐‘ฅ โˆˆ (๐œ‹/2 " , ฯ€" ) Thus, f is strictly decreasing in (๐œ‹/2 " ฯ€" ) Rough cos ๐œ‹/2 = 0 cos 3๐œ‹/4 = co๐‘  ("ฯ€ โˆ’ " ๐œ‹/4) = โ€“ cosโก๐œ‹/4 = (โˆ’1 )/โˆš2 Value of cos ๐‘ฅ < o for ๐‘ฅ โˆˆ (๐œ‹/2 , ๐œ‹) Ex 6.2, 3 Find the intervals in which the function f given by f (๐‘ฅ) = sin x is (c) neither increasing nor decreasing in (0, ฯ€)(0 , ฯ€) = (0 , ๐œ‹/2) โˆช (๐œ‹/2,๐œ‹) From 1st part f(๐‘ฅ) is strictly increasing in (0 , ๐œ‹/2) And from 2nd part f(๐‘ฅ) is strictly decreasing in (๐œ‹/2,๐œ‹) Thus, f(๐’™) is neither increasing nor decreasing in (0, ฯ€)

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.