Question 32 - CBSE Class 12 Sample Paper for 2021 Boards

Last updated at Oct. 27, 2020 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

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

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.

Question 32 - CBSE Class 12 Sample Paper for 2021 Boards

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 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