Find the intervals in which the function ๐‘“ given by ๐‘“(๐‘ฅ) = tan ๐‘ฅ − 4๐‘ฅ, ๐‘ฅ ∈ (0,π/2) is
(a) strictly increasing      (b) strictly decreasing

 

Find intervals in which function f(x) = tan x - 4x, is (a) strictly

Question 32 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2
Question 32 - CBSE Class 12 Sample Paper for 2021 Boards - Part 3

  1. Class 12
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Transcript

Question 32 Find the intervals in which the function ๐‘“ given by ๐‘“(๐‘ฅ) = tan ๐‘ฅ โˆ’ 4๐‘ฅ, ๐‘ฅ โˆˆ (0,๐œ‹/2) is (a) strictly increasing (b) strictly decreasing ๐‘“(๐‘ฅ) = tan ๐‘ฅ โˆ’ 4๐‘ฅ Finding ๐’‡^โ€ฒ (๐’™) ๐‘“^โ€ฒ (๐‘ฅ)=ใ€–๐‘ ๐‘’๐‘ใ€—^2 ๐‘ฅ โˆ’4 Putting ๐’‡^โ€ฒ (๐’™) = 0 ใ€–๐‘ ๐‘’๐‘ใ€—^2 ๐‘ฅ โˆ’4=0 ใ€–๐‘ ๐‘’๐‘ใ€—^2 ๐‘ฅ=4 ใ€–๐‘ ๐‘’๐‘ใ€—^2 ๐‘ฅ=2^2 ๐’”๐’†๐’„ ๐’™=ยฑ๐Ÿ Thus, ๐’™=๐…/๐Ÿ‘,๐Ÿ๐…/๐Ÿ‘,๐Ÿ’๐…/๐Ÿ‘,โ€ฆโ€ฆโ€ฆ Since ๐‘ฅ โˆˆ (0,๐œ‹/2) โˆด ๐’™= ๐…/๐Ÿ‘ Plotting points on Number line Hence, ๐‘“(๐‘ฅ) is is strictly decreasing in (๐ŸŽ,๐…/๐Ÿ‘) & ๐‘“(๐‘ฅ) is strictly increasing in (๐…/๐Ÿ‘,๐…/๐Ÿ)

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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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.