f x 3cos 3x Therefore f x 0 gives cos 3x 0 which or 3 0 17 2 into two disjoint intervals 0 implies 3x 0 Now f x 0 all xe T T fis increasing on or as x 2 Solution We have So x Therefore fis increasing in 0 0 is increasing or decreasing namely The points x BI6 Note that TC TU 4 TU 2 TC and x Ra R6 5T 3x TU Also the given function is continuous at x 0 and x 6 T The point x 6 B N 3 2 and decreasing on Rationalised 2023 24 and decreasing in T as 0 x 0 3x 6 Example 13 Find the intervals in which the function f given by f x sin x cos x 0 x 2 Now f x 0 gives sin x cos x which gives that 0 7 7 5 and ST 27 4 4 4 gives TU TU 6 2 f x sin x cos x f x cos x sin x TC x 0 if x 0 ST 3x 0 2 3 0 T 4 2 2 divides the interval 0 APPLICATION OF DERIVATIVES T T 6 2 as x 0 B 6 Fig 6 5 0 3x and f x 0 for 2 4 0 7 E2 ROBN TC T 5T 4 Fig 6 6 Therefore by Theorem 1 157 as 0 x 2 27 into three disjoint intervals e rejushed 2