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Ex 6.2, 12 (C) - Chapter 6 Class 12 Application of Derivatives (Term 1)
Last updated at March 16, 2023 by Teachoo
Ex 6.2
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Ex 6.2, 6 (a)
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Transcript
Ex 6.2, 12 Which of the following functions are strictly decreasing on (0,๐/2) ? (C) cos 3๐ฅ Let f(๐ฅ) = cos 3๐ฅ Finding fโ(๐) fโ(๐ฅ) = (cosโก3๐ฅ )โฒ fโ(๐ฅ) = โ3 sin 3๐ฅ Let 3๐ฅ = ฮธ โด fโ(๐ฅ) = โ3 sin ฮธ When 0 < x < ๐/2 , then 0 < ฮธ < ๐๐ /๐ For 0 < ฮธ < ๐๐ /๐ sin ฮธ is positive for 0 < ฮธ < ๐ sin ฮธ is negative for 0 < ฮธ < ๐๐ /๐ Thus, we can say that sin ฮธ is neither positive nor negative for 0 < ฮธ < ๐๐ /๐ Putting ฮธ = 3x sin 3x is neither positive nor negative for 0 < 3x < ๐๐ /๐ โ3 sin 3x is neither positive nor negative for 0 < 3x < 3๐/2 fโ(x) is neither positive nor negative for 0 < x < ๐ /๐ Thus, we can write that f(x) is neither increasing nor decreasing for ๐ โ (๐ , ๐ /๐)
