The length of a longest interval in which the function 3sin⁡x−4sin3⁡x is incresing is

Since 3sin⁡x−4sin3⁡x=sin⁡3x and sin⁡3x increases when 3x takes values from −π/2 to π/2 or x takes values from −π/6 to π/6. Thus, the length of the longest interval in  which 3sin⁡x−4sin3⁡x increases is π/6−(−π/6)=π/3.