Find the intervals in which the function 𝑓 given by 𝑓(π‘₯) = tan π‘₯ − 4π‘₯, π‘₯ ∈ (0,π/2) is
(a) strictly increasing      (b) strictly decreasing

 

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  1. Class 12
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Transcript

Question 32 Find the intervals in which the function 𝑓 given by 𝑓(π‘₯) = tan π‘₯ βˆ’ 4π‘₯, π‘₯ ∈ (0,πœ‹/2) is (a) strictly increasing (b) strictly decreasing 𝑓(π‘₯) = tan π‘₯ βˆ’ 4π‘₯ Finding 𝒇^β€² (𝒙) 𝑓^β€² (π‘₯)=〖𝑠𝑒𝑐〗^2 π‘₯ βˆ’4 Putting 𝒇^β€² (𝒙) = 0 〖𝑠𝑒𝑐〗^2 π‘₯ βˆ’4=0 〖𝑠𝑒𝑐〗^2 π‘₯=4 〖𝑠𝑒𝑐〗^2 π‘₯=2^2 𝒔𝒆𝒄 𝒙=±𝟐 Thus, 𝒙=𝝅/πŸ‘,πŸπ…/πŸ‘,πŸ’π…/πŸ‘,……… Since π‘₯ ∈ (0,πœ‹/2) ∴ 𝒙= 𝝅/πŸ‘ Plotting points on Number line Hence, 𝑓(π‘₯) is is strictly decreasing in (𝟎,𝝅/πŸ‘) & 𝑓(π‘₯) is strictly increasing in (𝝅/πŸ‘,𝝅/𝟐)

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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.