Ex 6.2, 12 Which of the following functions are strictly decreasing on (0,𝜋/2) ? (B) cos 2𝑥 Let f(𝑥) = cos 2𝑥 Finding f’(𝒙) f’(𝑥) = (cos⁡2𝑥 )′ f’(𝑥) = –2 sin 2𝑥 Let 2𝑥 = θ ∴ f’(𝑥) = –2 sin θ When 0 < x < 𝜋/2 , then 0 < θ < 𝜋 Since sin θ > 0 for 0 < θ < 𝜋 Therefore, sin 2x > 0 for 0 < 2x < 𝜋 Multiplying −2 both sides −2 × sin 2x < −2 × 0 for 0 < 2x < 𝜋 −2 sin 2x < 0 for 0 < 2x < 𝜋 f’(x) < 0 for 0 < 2x < 𝜋 f’(x) < 0 for 0 < x < 𝝅/𝟐 Therefore, f(x) is strictly decreasing for 𝒙 ∈ (𝟎 , 𝝅/𝟐)

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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