Example 9 - Prove that f(x) = cos x is (a) strictly decreasing - Examples

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  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, ) f( ) = cos f ( ) = sin Since, sin > 0 for (0, ) So, sin < 0 for (0, ) f ( ) < 0 for (0 , ) So f is Strictly decreasing in (0 , ) Example 9 Prove that the function given by f (x) = cos x is (b) strictly increasing in ( , 2 ), and f ( ) = cos f ( ) = sin Note:- sin < 0 for ( , 2 ) So, sin > 0 for ( , 2 ) f ( ) > 0 for ( , 2 ) So, f is strictly increasing in ( , 2 ) Example 9 Prove that the function given by f (x) = cos x is (c) neither increasing nor decreasing in (0, 2 ). (0 , 2 ) = (0 , ) ( , 2 ) From 1st part f ( ) is strictly decreasing in (0 , ) & from 2nd part f ( ) is strictly increasing in ( , 2 ) Thus f ( ) is neither increasing nor decreasing in (0 , 2 )

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.