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Ex 6.2,12 - Chapter 6 Class 12 Application of Derivatives - Part 4

Ex 6.2,12 - Chapter 6 Class 12 Application of Derivatives - Part 5
Ex 6.2,12 - Chapter 6 Class 12 Application of Derivatives - Part 6

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Ex 6.2, 12 Which of the following functions are strictly decreasing on (0,πœ‹/2) ? (C) cos 3π‘₯ Let f(π‘₯) = cos 3π‘₯ Finding f’(𝒙) f’(π‘₯) = (cos⁑3π‘₯ )β€² f’(π‘₯) = –3 sin 3π‘₯ Let 3π‘₯ = ΞΈ ∴ f’(π‘₯) = –3 sin ΞΈ When 0 < x < πœ‹/2 , then 0 < ΞΈ < πŸ‘π…/𝟐 For 0 < ΞΈ < πŸ‘π…/𝟐 sin ΞΈ is positive for 0 < ΞΈ < πœ‹ sin ΞΈ is negative for 0 < ΞΈ < πŸ‘π…/𝟐 Thus, we can say that sin ΞΈ is neither positive nor negative for 0 < ΞΈ < πŸ‘π…/𝟐 Putting ΞΈ = 3x sin 3x is neither positive nor negative for 0 < 3x < πŸ‘π…/𝟐 βˆ’3 sin 3x is neither positive nor negative for 0 < 3x < 3πœ‹/2 f’(x) is neither positive nor negative for 0 < x < 𝝅/𝟐 Thus, we can write that f(x) is neither increasing nor decreasing for 𝒙 ∈ (𝟎 , 𝝅/𝟐)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.