Ex 6.2, 5 - Find intervals f(x) = 2x3 - 3x2 - 36x + 7 - 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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Ex 6.2,5 Find the intervals in which the function f given by f ( ) = 2 3 3 2 36 + 7 is (a) strictly increasing (b) strictly decreasing f ( ) = 2 3 3 2 36 + 7 Step 1: Calculating f ( ) f ( ) = 2 3 3 2 36 + 7 f ( ) = 6 2 6 36 + 0 f ( ) = 6 ( 2 6 ) f ( ) = 6( 2 3 + 2 6) = 6( 3) ( + 2) Step 2: Putting f ( ) = 0 6( + 2) )( 3) = 0 ( + 2) ( 3) = 0 6 ( + 2) ( 3) = 0 So, x = 2 & x = 3 Step 3: Plotting point on real line Points 2 , & 3 divide the real line into 3 disjoint intervals i.e. ( 2) ( 2 , 3) & (3 , Step 4: (a) f is strictly increasing in ( , 2) & (3 , ) (b) f is strictly decreasing in ( 2 , 3)

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