Misc 7 - Chapter 6 Class 12 Application of Derivatives

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Misc 7 Find the intervals in which the function f given by f (x) = x3 + 1 3 , 0 is (i) increasing (ii) decreasing. f = 3 + 1 3 Step 1: Finding f f = 3 + 3 . = 3 2 + 3 3 1 = 3 2 3 4 = 3 2 3 4 = 3 2 1 4 Step 2: Putting f = 0 3 2 1 4 = 0 2 1 4 = 0 6 1 4 = 0 6 1 = 0 3 2 1 2 =0 3 1 3 +1 =0 Hence, = 1 & 1 Step 3: Plotting value of on real line Thus, = 1 & 1 divide the real line into three disjoint intervals i.e. 1 1, 1 & 1, Hence, f is strictly increasing on & , & strictly decreasing on ,