Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Last updated at April 15, 2021 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Transcript

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, βsin 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, 2Ο), and f (π₯) = cos π₯ fβ(π) = β sin π Since 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) βͺ (Ο , 2Ο) From 1st part f(π₯) is strictly decreasing in (0 , Ο) And from 2nd part f(π₯) is strictly increasing in (Ο , 2Ο) Thus, f(π) is neither increasing nor decreasing in (0, 2Ο)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.