# Example 13 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 13 Find the intervals in which the function f given by f = sin + cos , 0 2 is strictly increasing or strictly decreasing. f = sin + cos 0 x 2 Step 1: Finding f f = sin x + cos f = (sin + cos ) f = sin + cos f = cos + f = cos sin Step 2: Putting f = 0 cos sin = 0 cos = sin = 4 , 5 4 0 2 Step 3: Plotting points Points = 4 , 5 4 divide interval 0 , 2 into 3 disjoint intervals 0 , 4 , 4 , 5 4 , 5 4 , 2 Step 4: Checking sign of f = cos sin Case 1 When 0 , 4 as 0 < 4 Thus, f > 0 for 0 , 4 Case 2 When 4 , 5 4 As 4 < x < 5 4 Let us find value of f (x) at any value of lies between 4 , 5 4 f < 0 for 4 , 5 4 Case 3 When 5 4 , 2 as 5 4 < 2 At = 2 f = cos sin f 2 = cos 2 sin 2 = cos + 0 = cos 0 = 1 0 = 1 > 0 So, f > 0 at = 2 Hence f (x) > 0 for 5 4 , 2 Thus, f is strictly increasing intervals , & , f is strictly increasing intervals ,

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Chapter 6 Class 12 Application of Derivatives

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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.