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

Last updated at Jan. 7, 2020 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΄ f (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) Rough sin Ο = 0 sin 5π/4 = sin ("Ο + " π/4) = βsin (π/4) = (β1)/β2 sin 2Ο = sin (Ο + Ο ) = β sin Ο = 0 Value of sin π₯ < 0 for π₯ β (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) & 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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Chapter 6 Class 12 Application of Derivatives

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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.