Example 13 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 14, 2019 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 ,
Examples
Example 1
Example 2
Example 3
Example 4 Important
Example 5
Example 6
Example 7
Example 8 Important
Example 9 Important
Example 10
Example 11 Important
Example 12
Example 13 Important You are here
Example 14
Example 15
Example 16
Example 17 Important
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Example 25
Example 26
Example 27
Example 28 Important
Example 29
Example 30 Important
Example 31
Example 32 Important
Example 33 Important
Example 34
Example 35 Important
Example 36
Example 37 Important
Example 38 Important
Example 39
Example 40 Important
Example 41 Important
Example 42 Important
Example 43 Important
Example 44 Important
Example 45 Important
Example 46 Important
Example 47 Important
Example 48 Important
Example 49
Example 50 Important
Example 51
Chapter 6 Class 12 Application of Derivatives
Serial order wise
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.