Let the f : R → R be defined by f (x) = 2x + cos x, then f :
(A) has a minimum at x = π (B) has a maximum, at x = 0
(C) is a decreasing function (D) is an increasing function
Last updated at Nov. 23, 2021 by Teachoo
Transcript
Question 18 Let the f : R β R be defined by f (x) = 2x + cos x, then f : (A) has a minimum at x = π (B) has a maximum, at x = 0 (C) is a decreasing function (D) is an increasing function Given f (π) = 2π + cos π Since we need to check If it is increasing or decreasing Or, at what value of π₯ the function has maximum or minimum value Thus, we check sign of πβ²(π) β΄ Differentiating π(π₯) w.r.t. π₯ f (π₯) = 2π₯ + cos π₯ fβ (π) = 2 β sin π Checking sign of πβ²(π) We know that β1 β€ sin π β€ 1 Multiplying by β1 β1 Γ (β1) β₯ βsin π₯ β₯ 1 Γ (β1) 1 β₯ β sin π₯ β₯ β1 β1 β€ β sin π β€ 1 Adding 2 both sides 2 β 1 β€ 2 β sin π₯ β€ 2 + 1 1 β€ 2 β sin π β€ 3 1 β€ πβ²(π)β€ 3 β΄ πβ²(π) > 0 Thus, f (π₯) is increasing function So, the correct answer is (D)
NCERT Exemplar - MCQs
Question 2
Question 3 Important
Question 4
Question 5
Question 6 Important
Question 7 Important
Question 8
Question 9 Important
Question 10
Question 11 Important
Question 12 Important
Question 13
Question 14
Question 15
Question 16 Important
Question 17 Important
Question 18 Important You are here
Question 19
Question 20 Important
Question 21 Important
Question 22 Important
Question 23
Question 24 Important
Question 25 Important
Question 26
Question 27
Question 28 Important
Question 29 Important
Question 30 Important
NCERT Exemplar - MCQs
About the Author