Question 32 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Find the intervals in which the function 𝑓 given by 𝑓(𝑥) = tan 𝑥 − 4𝑥, 𝑥 ∈ (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

Transcript

Question 32 Find the intervals in which the function 𝑓 given by 𝑓(𝑥) = tan 𝑥 − 4𝑥, 𝑥 ∈ (0,𝜋/2) is (a) strictly increasing (b) strictly decreasing 𝑓(𝑥) = tan 𝑥 − 4𝑥 Finding 𝒇^′ (𝒙) 𝑓^′ (𝑥)=〖𝑠𝑒𝑐〗^2 𝑥 −4 Putting 𝒇^′ (𝒙) = 0 〖𝑠𝑒𝑐〗^2 𝑥 −4=0 〖𝑠𝑒𝑐〗^2 𝑥=4 〖𝑠𝑒𝑐〗^2 𝑥=2^2 𝒔𝒆𝒄 𝒙=±𝟐 Thus, 𝒙=𝝅/𝟑,𝟐𝝅/𝟑,𝟒𝝅/𝟑,……… Since 𝑥 ∈ (0,𝜋/2) ∴ 𝒙= 𝝅/𝟑 Plotting points on Number line Hence, 𝑓(𝑥) is is strictly decreasing in (𝟎,𝝅/𝟑) & 𝑓(𝑥) is strictly increasing in (𝝅/𝟑,𝝅/𝟐)

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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