CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Question 20 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Sept. 4, 2021 by Teachoo

The least value of the function π(π₯) = 2 πππ π₯ + π₯ in the closed interval [0, π/2] is:

(a) 2 (b) π/2 + √3
(c) π/2 (d) The least value does not exist

Question 20 The least value of the function π(π₯) = 2 πππ π₯ + π₯ in the closed interval ["0," π/2] is: (a) 2 (b) π/2 + β3 (c) π/2 (d) The least value does not exist
Let f(π₯)="2 πππ π₯ + π₯"
Finding fβ(π)
πβ(π₯)=π(2 cosβ‘π₯ + π₯)/ππ₯
=β2 sinβ‘π₯+1
Putting fβ(π)=π
β2 sinβ‘π₯+1=0
2 sin π₯=1
sin π₯=1/2
β΄ x = π /π
Since we are given closed interval ["0," π /π]
Letβs check value of f(x) at 0, π /π and π /π
f(0) = 2 cos 0 + 0 = 2 Γ 1 + 0 = 2
f(π /π) = 2 cos π /π + π /π = 2 Γ β3/2 + π /π = β3 + π /π
f(π /π) = 2 cos π /π + π /π = 2 Γ 0 + π /π = π /π
Since value of f(x) is lowest at x = π /π
So, the correct answer is (C)

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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.