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Ex 6.2, 3 - Find the intervals in which f(x) = sin x - Ex 6.2

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Ex 6.2,3 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Ex 6.2,3 - Chapter 6 Class 12 Application of Derivatives - Part 3

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Ex 6.2, 3 Find the intervals in which the function f given by f (𝑥) = sin 𝑥 is (a) strictly increasing in (0 , 𝜋/2) f(𝑥) = sin 𝑥 f’(𝒙) = cos 𝒙 Since cos 𝑥 > 0 for 𝑥 ∈ ("0 , " 𝜋/2) ∴ f’(𝑥) < 0 for 𝑥 ∈ (0 , π) Thus, f is strictly increasing in ("0 , " 𝜋/2) Rough cos 0 = 1 cos 𝜋/4 = 1/√2 cos 𝜋/2 = 0 Value of cos⁡𝑥 > 0 for (0 , 𝜋/2) Ex 6.2, 3 Find the intervals in which the function f given by f (𝑥) = Sin x is (b) strictly decreasing (𝜋/2,𝜋)f(𝑥) = sin 𝑥 f’(𝒙) = cos 𝒙 Since cos 𝑥 < 0 for 𝑥 ∈ (𝜋/2 , 𝜋) ∴ f’(𝑥) < 0 for 𝑥 ∈ (𝜋/2 " , π" ) Thus, f is strictly decreasing in (𝜋/2 " π" ) Rough cos 𝜋/2 = 0 cos 3𝜋/4 = co𝑠 ("π − " 𝜋/4) = – cos⁡𝜋/4 = (−1 )/√2 Value of cos 𝑥 < o for 𝑥 ∈ (𝜋/2 , 𝜋) Ex 6.2, 3 Find the intervals in which the function f given by f (𝑥) = sin x is (c) neither increasing nor decreasing in (0, π)(0 , π) = (0 , 𝜋/2) ∪ (𝜋/2,𝜋) From 1st part f(𝑥) is strictly increasing in (0 , 𝜋/2) And from 2nd part f(𝑥) is strictly decreasing in (𝜋/2,𝜋) Thus, f(𝒙) is neither increasing nor decreasing in (0, π)

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