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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 March 22, 2023 by

The value of 𝑏 for which the function 𝑓(π‘₯) = π‘₯ + π‘π‘œπ‘  π‘₯ + 𝑏 is strictly decreasing over R is:

(a) 𝑏 < 1Β  (b) No value of b exists

(c) 𝑏 ≀ 1Β  (d) 𝑏 β‰₯ 1

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Question 29 The value of 𝑏 for which the function 𝑓(π‘₯) = π‘₯ + π‘π‘œπ‘  π‘₯ + 𝑏 is strictly decreasing over R is: (a) 𝑏 < 1 (b) No value of b exists (c) 𝑏 ≀ 1 (d) 𝑏 β‰₯ 1 Given 𝑓(π‘₯) = π‘₯ + π‘π‘œπ‘  π‘₯ + 𝑏 Now, 𝑓’(π‘₯) = 1 βˆ’ sin x Since 𝑓(π‘₯) is strictly decreasing over R 𝑓’(π‘₯) < 0 1 βˆ’ sin x < 0 1 < sin x sin x > 1 Since βˆ’1 ≀ sin x ≀ 1 Thus, sin x > 1 is not possible Thus, for no value of b, 𝑓(π‘₯) is strictly decreasing So, the correct answer is (B)

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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.