Question 18 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at Dec. 4, 2021 by Teachoo

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Let the f :
R
β
R
be defined by f (x) = 2x + cos x, then f :

(A) has a minimum at x = ΟΒ Β Β Β Β (B) has a maximum, at x = 0

(C) is a decreasing functionΒ Β Β Β Β (D) is an increasing function

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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)

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