##
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

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Chapter 6 Class 12 Application of Derivatives

Serial order wise

Last updated at April 16, 2024 by Teachoo

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 (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)