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Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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 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.