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

Slide102.jpeg

Slide103.jpeg

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Question 26 The maximum value of sin x . cos x is (A) 1/4 (B) 1/2 (C) √2 (D) 2 √2 Let f(𝒙)=sin⁑π‘₯βˆ™cos⁑π‘₯ =(2 sin⁑π‘₯ cos⁑π‘₯)/2 =(π’”π’Šπ’ πŸπ’™)/𝟐 Since, βˆ’πŸβ‰€π’”π’Šπ’ πœ½β‰€πŸ Putting πœƒ=2π‘₯ βˆ’1≀sin⁑2π‘₯≀1 Dividing by 2 βˆ’1/2≀(𝑠𝑖𝑛 2π‘₯)/2≀1/2 βˆ’πŸ/πŸβ‰€π’‡(𝒙)β‰€πŸ/𝟐 ∴ Maximum value of 𝑓(π‘₯) is 𝟏/𝟐. So, the correct answer is (B).

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
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.