Check sibling questions

Question 22 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at March 16, 2023 by

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

Slide86.JPG

Slide87.JPG
Slide88.JPG

This video is only available for Teachoo black users

Subscribe Now

This video is only available for Teachoo black users

Subscribe Now

Get live Maths 1-on-1 Classs - Class 6 to 12

Book 30 minute class for β‚Ή 499 β‚Ή 299

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)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.