Ex 6.2,3 - Chapter 6 Class 12 Application of Derivatives

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Ex 6.2,3 Find the intervals in which the function f given by f ( ) = Sin is (a) strictly increasing in 0 , 2 f ( ) = sin f ( ) = cos Since cos > 0 for 0 , 2 So, f ( ) > 0 for 0 , 2 Thus, f is strictly increasing in 0 , 2 Ex 6.2,3 Find the intervals in which the function f given by f ( ) = Sin x is (b) strictly decreasing 2 , f ( ) = sin f ( ) = cos Since cos < 0 for 2 , So, f ( ) < 0 for 2 , Thus, f is strictly decreasing in 2 Ex 6.2,3 Find the intervals in which the function f given by f ( ) = Sin x is (c)neither increasing nor decreasing in (0 , ) Step 1: f ( ) = sin f ( ) = cos Step 2: Putting f ( ) = 0 cos x= 0 = 2 Step 3: Since (0 , ) we start number line from 0 to The point = 2 divides the interval (0 , ) into two disjoint interval i.e. 0 , 2 , 2 From 1st part , f ( ) is strictly increasing in 0 2 & from 2nd part, f( ) is strictly decreasing in 2 Hence f( ) is neither increasing nor decreasing in (0 , )