CBSE Class 12 Sample Paper for 2021 Boards
You are here
CBSE Class 12 Sample Paper for 2021 Boards
Last updated at August 14, 2026 by Teachoo
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)
