Ex 6.2,19 - Chapter 6 Class 12 Application of Derivatives

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Ex 6.2,19 The interval in which = 2 is increasing is (A) ( , ) (B) ( 2, 0) (C) (2, ) (D) (0, 2) Let f = 2e Step 1: Finding f f = 2 f = 2 e + 2 f = 2 e + 2 f = 2 e- e- 2 f = e 2 Step 2: Putting f =0 e- 2 = 0 2 = 0 So, =0 & = 2 Step 3: Plotting points on real line The points = 0 & 2 divide the real line into 3 disjoint intervals i.e 0 , 0 , 2 & 2 , uc1 Step 4: Hence f is strictly decreasing on 0 & 2 , uc1 & f is strictly increasing on 0 , 2 Hence correct answer is