Ex 6.2, 12 (B) - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Ex 6.2
Ex 6.2, 1
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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)
