Ex 6.2, 12 (B) - Chapter 6 Class 12 Application of Derivatives (Term 1)
Last updated at Aug. 19, 2021 by
Transcript
Ex 6.2, 12 Which of the following functions are strictly decreasing on (0,π/2) ? (B) cos 2π₯ Let f(π₯) = cos 2π₯ Finding fβ(π) fβ(π₯) = (cosβ‘2π₯ )β² fβ(π₯) = β2 sin 2π₯ Let 2π₯ = ΞΈ β΄ fβ(π₯) = β2 sin ΞΈ When 0 < x < π/2 , then 0 < ΞΈ < π Since sin ΞΈ > 0 for 0 < ΞΈ < π Therefore, sin 2x > 0 for 0 < 2x < π Multiplying β2 both sides β2 Γ sin 2x < β2 Γ 0 for 0 < 2x < π β2 sin 2x < 0 for 0 < 2x < π fβ(x) < 0 for 0 < 2x < π fβ(x) < 0 for 0 < x < π /π Therefore, f(x) is strictly decreasing for π β (π , π /π)
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 You are here
Ex 6.2, 12 (C) Important
Ex 6.2, 12 (D)
Ex 6.2, 13 (MCQ) Important
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Ex 6.2,19 (MCQ) Important
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