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Ex 6.2
Ex 6.2,2
Ex 6.2,3 Important
Ex 6.2,4
Ex 6.2, 5 Important
Ex 6.2, 6 (a)
Ex 6.2, 6 (b) Important
Ex 6.2, 6 (c) Important
Ex 6.2, 6 (d)
Ex 6.2, 6 (e) Important
Ex 6.2, 7
Ex 6.2,8 Important
Ex 6.2,9 Important
Ex 6.2,10
Ex 6.2,11
Ex 6.2, 12 (A)
Ex 6.2, 12 (B) Important You are here
Ex 6.2, 12 (C) Important
Ex 6.2, 12 (D)
Ex 6.2, 13 (MCQ) Important
Ex 6.2,14 Important
Ex 6.2,15
Ex 6.2, 16
Ex 6.2,17 Important
Ex 6.2,18
Ex 6.2,19 (MCQ) Important
Last updated at May 29, 2023 by Teachoo
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) = (cos2𝑥 )′ 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)