Ex 6.2

Chapter 6 Class 12 Application of Derivatives
Serial order wise

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Ex 6.2, 3 Find the intervals in which the function f given by f (đĽ) = sin đĽ is (a) strictly increasing in (0 , đ/2) f(đĽ) = sin đĽ fâ(đ) = cos đ Since cos đĽ > 0 for đĽ â ("0 , " đ/2) â´ fâ(đĽ) < 0 for đĽ â (0 , Ď) Thus, f is strictly increasing in ("0 , " đ/2) Rough cos 0 = 1 cos đ/4 = 1/â2 cos đ/2 = 0 Value of cosâĄđĽ > 0 for (0 , đ/2) Ex 6.2, 3 Find the intervals in which the function f given by f (đĽ) = Sin x is (b) strictly decreasing (đ/2,đ)f(đĽ) = sin đĽ fâ(đ) = cos đ Since cos đĽ < 0 for đĽ â (đ/2 , đ) â´ fâ(đĽ) < 0 for đĽ â (đ/2 " , Ď" ) Thus, f is strictly decreasing in (đ/2 " Ď" ) Rough cos đ/2 = 0 cos 3đ/4 = cođ  ("Ď â " đ/4) = â cosâĄđ/4 = (â1 )/â2 Value of cos đĽ < o for đĽ â (đ/2 , đ) Ex 6.2, 3 Find the intervals in which the function f given by f (đĽ) = sin x is (c) neither increasing nor decreasing in (0, Ď)(0 , Ď) = (0 , đ/2) âŞ (đ/2,đ) From 1st part f(đĽ) is strictly increasing in (0 , đ/2) And from 2nd part f(đĽ) is strictly decreasing in (đ/2,đ) Thus, f(đ) is neither increasing nor decreasing in (0, Ď)