Ex 6.2, 12 (C) - Chapter 6 Class 12 Application of Derivatives
Last updated at April 16, 2024 by Teachoo
Ex 6.2
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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
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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
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Ex 6.2,17 Important
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Ex 6.2,19 (MCQ) Important
Transcript
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)
