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Question 5 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

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

Transcript

Question 5 Let the f : R β†’ R be defined by f (x) = 2x + cos x, then f : (A) has a minimum at x = πœ‹ (B) has a maximum, at x = 0 (C) is a decreasing function (D) is an increasing function Given f (𝒙) = 2𝒙 + cos 𝒙 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 𝒇′(𝒙) ∴ Differentiating 𝑓(π‘₯) w.r.t. π‘₯ f (π‘₯) = 2π‘₯ + cos π‘₯ f’ (𝒙) = 2 βˆ’ sin 𝒙 Checking sign of 𝒇′(𝒙) We know that βˆ’1 ≀ sin 𝒙 ≀ 1 Multiplying by βˆ’1 βˆ’1 Γ— (βˆ’1) β‰₯ βˆ’sin π‘₯ β‰₯ 1 Γ— (βˆ’1) 1 β‰₯ βˆ’ sin π‘₯ β‰₯ βˆ’1 βˆ’1 ≀ βˆ’ sin 𝒙 ≀ 1 Adding 2 both sides 2 βˆ’ 1 ≀ 2 βˆ’ sin π‘₯ ≀ 2 + 1 1 ≀ 2 βˆ’ sin 𝒙 ≀ 3 1 ≀ 𝒇′(𝒙)≀ 3 ∴ 𝒇′(𝒙) > 0 Thus, f (π‘₯) is increasing function So, the correct answer is (D)
  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

    3. NCERT Exemplar - MCQs

    Tangents and Normals (using Differentiation) →
Tangents and Normals (using Differentiation) →
Chapter 6 Class 12 Application of Derivatives
Serial order wise

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo