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

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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)

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.