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Ex 6.2

Ex 6.2, 1

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

Ex 6.2, 12 (C) Important You are here

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) ? (C) cos 3𝑥 Let f(𝑥) = cos 3𝑥 Finding f’(𝒙) f’(𝑥) = (cos3𝑥 )′ f’(𝑥) = –3 sin 3𝑥 Let 3𝑥 = θ ∴ f’(𝑥) = –3 sin θ When 0 < x < 𝜋/2 , then 0 < θ < 𝟑𝝅/𝟐 For 0 < θ < 𝟑𝝅/𝟐 sin θ is positive for 0 < θ < 𝜋 sin θ is negative for 0 < θ < 𝟑𝝅/𝟐 Thus, we can say that sin θ is neither positive nor negative for 0 < θ < 𝟑𝝅/𝟐 Putting θ = 3x sin 3x is neither positive nor negative for 0 < 3x < 𝟑𝝅/𝟐 −3 sin 3x is neither positive nor negative for 0 < 3x < 3𝜋/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)