Ex 6.2, 12 (C) - 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) ? (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)
