Ex 6.2, 12 (C) - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 6.2, 12 Which of the following functions are strictly decreasing on (0,π/2) ? (C) cos 3π₯ Let f(π₯) = cos 3π₯ Finding fβ(π) fβ(π₯) = (cosβ‘3π₯ )β² fβ(π₯) = β3 sin 3π₯ Let 3π₯ = ΞΈ β΄ fβ(π₯) = β3 sin ΞΈ When 0 < x < π/2 , then 0 < ΞΈ < ππ /π For 0 < ΞΈ < ππ /π sin ΞΈ is positive for 0 < ΞΈ < π sin ΞΈ is negative for 0 < ΞΈ < ππ /π Thus, we can say that sin ΞΈ is neither positive nor negative for 0 < ΞΈ < ππ /π Putting ΞΈ = 3x sin 3x is neither positive nor negative for 0 < 3x < ππ /π β3 sin 3x is neither positive nor negative for 0 < 3x < 3π/2 fβ(x) is neither positive nor negative for 0 < x < π /π Thus, we can write that f(x) is neither increasing nor decreasing for π β (π , π /π)
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