Question 13 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by Teachoo

The maximum value of sin x . cos x is

(A) 1/4 (B) 1/2

(C) √2 (D) 2 √2

This question is similar to Ex 6.5, 9 - Chapter 6 Class 12 - Application of Derivatives

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Transcript

Question 13 The maximum value of sin x . cos x is (A) 1/4 (B) 1/2 (C) √2 (D) 2 √2 Let f(𝒙)=sin⁡𝑥∙cos⁡𝑥 =(2 sin⁡𝑥 cos⁡𝑥)/2 =(𝒔𝒊𝒏 𝟐𝒙)/𝟐 Since, −𝟏≤𝒔𝒊𝒏 𝜽≤𝟏 Putting 𝜃=2𝑥 −1≤sin⁡2𝑥≤1 Dividing by 2 −1/2≤(𝑠𝑖𝑛 2𝑥)/2≤1/2 −𝟏/𝟐≤𝒇(𝒙)≤𝟏/𝟐 ∴ Maximum value of 𝑓(𝑥) is 𝟏/𝟐. So, the correct answer is (B).

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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

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