NCERT Exemplar - MCQs

Chapter 6 Class 12 Application of Derivatives
Serial order wise

## (D) sometimes increases and sometimes decreases.

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

### Transcript

Question 9 The function f (x) = tan x – x always increases (B) always decreases (C) never increases (D) sometimes increases and sometimes decreases. Given 𝑓(𝑥) = tan 𝑥 − 𝑥 Finding 𝒇^′ (𝒙) 𝑓^′ (𝑥)=〖𝒔𝒆𝒄〗^𝟐 𝒙 −𝟏 Now, we need to check if 𝒇(𝒙) is increasing or decreasing Checking sign of 𝒇^′ (𝒙) 𝑓^′ (𝑥)=〖𝒔𝒆𝒄〗^𝟐 𝒙 −𝟏 Now, 𝐬𝐞𝐜 𝒙 𝝐 (−∞,−𝟏]∪[𝟏,∞) So, 〖𝒔𝒆𝒄〗^𝟐 𝒙 𝜖 [1,∞) Therefore, we can write this as 𝟏≤〖𝒔𝒆𝒄〗^𝟐 𝒙≤∞ 1−𝟏≤〖𝑠𝑒𝑐〗^2 𝑥−𝟏≤∞−𝟏 0≤〖𝒔𝒆𝒄〗^𝟐 𝒙−𝟏≤∞ Thus, 〖𝑠𝑒𝑐〗^2 𝑥−1≥0 ∴ 𝒇^′ (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 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.