Example 13 - Find intervals where f(x) = sin x + cos x is - Find intervals of increasing/decreasing

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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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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