Find the intervals in which f(x) = sin 3x is increasing and decreasing in the interval [0, pie/2]. Share with your friends Share 2 Varun.Rawat answered this We have, fx = sin 3x⇒f'x = 3 cos 3xNow, f'x = 0⇒3 cos 3x = 0⇒cos 3x = 0⇒cos 3x = cos π2 and cos 3x = cos 3π2⇒3x = π2 or 3x = 3π2⇒x = π6 or x =π2Now, x = π6 divides the interval 0, π2 into 2 disjoint intervals :[0, π/6) and (π/6, π/2].Consider the interval 0≤x<π6.When 0≤x<π6⇒3×0≤3x<3×π6⇒0≤3x<π2Now, cos 3x > 0 , when 0≤3x<π2⇒3 cos 3x > 0, when 0≤3x<π2⇒f'x > 0, when 0≤3x<π2 or 0≤x<π6So, fx is increasing in the interval [0, π/6).Consider the interval π6<x≤π2.When π6<x≤π2⇒3×π6≤3x<3×π2⇒π2<3x≤3π2Now, cos 3x < 0 , when π2<3x≤3π2⇒3 cos 3x < 0, when π2<3x≤3π2⇒f'x < 0, when π2<3x≤3π2 or π6<x≤π2So, fx is decreasing in the interval (π/6, π/2]. -5 View Full Answer