Ex 6.2,11 - Chapter 6 Class 12 Application of Derivatives

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Ex 6.2,11 Prove that the function f given by f ( ) = 2 + 1 is neither strictly increasing nor strictly decreasing on ( 1, 1). Let f = 2 + 1 1 , 1 Step 1: Finding f f = 2 1 Step 2: Putting f = 0 2 1 = 0 2 = 1 = 1 2 Since 1 , 1 The point = 1 2 divide the intervals 1 , 1 into two disjoint intervals. i.e. 1 , 1 2 & 1 2 , 1 Hence f < 0 for 1 , 1 2 & f > 0 for 1 2 , 1 Hence f is neither decreasing nor increasing on , . Hence Proved