1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards
  3. CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
Check sibling questions

Question 29 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

The value of 𝑏 for which the function 𝑓(𝑥) = 𝑥 + 𝑐𝑜𝑠 𝑥 + 𝑏 is strictly decreasing over R is:

(a) 𝑏 < 1  (b) No value of b exists

(c) 𝑏 ≤ 1  (d) 𝑏 ≥ 1

Transcript

Question 29 The value of 𝑏 for which the function 𝑓(𝑥) = 𝑥 + 𝑐𝑜𝑠 𝑥 + 𝑏 is strictly decreasing over R is: (a) 𝑏 < 1 (b) No value of b exists (c) 𝑏 ≤ 1 (d) 𝑏 ≥ 1 Given 𝑓(𝑥) = 𝑥 + 𝑐𝑜𝑠 𝑥 + 𝑏 Now, 𝑓’(𝑥) = 1 − sin x Since 𝑓(𝑥) is strictly decreasing over R 𝑓’(𝑥) < 0 1 − sin x < 0 1 < sin x sin x > 1 Since −1 ≤ sin x ≤ 1 Thus, sin x > 1 is not possible Thus, for no value of b, 𝑓(𝑥) is strictly decreasing So, the correct answer is (B)
  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

    3. CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

    CBSE Class 12 Sample Paper for 2021 Boards →
CBSE Class 12 Sample Paper for 2021 Boards →
Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

About the Author

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 and Computer Science at Teachoo