1. Chapter 6 Class 12 Application of Derivatives
2. Serial order wise

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Example 9 Prove that the function given by f (x) = cos x is (a) strictly decreasing in (0, Ο) f(π₯) = cos π₯ fβ (π₯) = β sin π₯ Since, sin π₯ > 0 for π₯ β (0, Ο) So, βsin π < 0 for π₯ β (0, Ο) β΄ fβ (π₯) < 0 for π₯ β (0 , Ο) So f is Strictly decreasing in (0 , Ο) Example 9 Prove that the function given by f (x) = cos x is (b) strictly increasing in (Ο, 2 Ο), and f (π₯) = cos π₯ fβ (π₯) = β sin π₯ Note:- sin π₯ < 0 for π₯ β (Ο , 2Ο) So, β sin π > 0 for π₯ β (Ο , 2Ο) β fβ(π₯) > 0 for π₯ β (Ο , 2Ο) So, f is strictly increasing in (Ο , 2Ο) Example 9 Prove that the function given by f (x) = cos x is (c) neither increasing nor decreasing in (0, 2Ο). (0 , 2Ο) = (0 , Ο) βͺ (Ο , 2Ο) From 1st part f (π₯) is strictly decreasing in (0 , Ο) & from 2nd part f (π₯) is strictly increasing in (Ο , 2Ο) Thus f (π) is neither increasing nor decreasing in (0 , 2Ο)