Check sibling questions

The function f (x) = tan x – x

(A)always increases Β 

(B) always decreases

(C) never increases

(D) sometimes increases and sometimes decreases.

Β 

This question is similar to Question 32 CBSE Class 12 Sample Paper 2021 Boards - Application of Derivatives

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Transcript

Question 22 The function f (x) = tan x – x always increases (B) always decreases (C) never increases (D) sometimes increases and sometimes decreases. Given 𝑓(π‘₯) = tan π‘₯ βˆ’ π‘₯ Finding 𝒇^β€² (𝒙) 𝑓^β€² (π‘₯)=〖𝒔𝒆𝒄〗^𝟐 𝒙 βˆ’πŸ Now, we need to check if 𝒇(𝒙) is increasing or decreasing Checking sign of 𝒇^β€² (𝒙) 𝑓^β€² (π‘₯)=〖𝒔𝒆𝒄〗^𝟐 𝒙 βˆ’πŸ Now, 𝐬𝐞𝐜 𝒙 𝝐 (βˆ’βˆž,βˆ’πŸ]βˆͺ[𝟏,∞) So, 〖𝒔𝒆𝒄〗^𝟐 𝒙 πœ– [1,∞) Therefore, we can write this as πŸβ‰€γ€–π’”π’†π’„γ€—^𝟐 π’™β‰€βˆž 1βˆ’πŸβ‰€γ€–π‘ π‘’π‘γ€—^2 π‘₯βˆ’πŸβ‰€βˆžβˆ’πŸ 0≀〖𝒔𝒆𝒄〗^𝟐 π’™βˆ’πŸβ‰€βˆž Thus, 〖𝑠𝑒𝑐〗^2 π‘₯βˆ’1β‰₯0 ∴ 𝒇^β€² (𝒙)>𝟎 for all values of x Hence, 𝒇(𝒙) always increases. So, the correct answer is (A)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.