Question

The length of a longest interval in which the function $3 \, \sin \, x - 4 \, \sin^3x$ is increasing, is

• A. $\frac{\pi}{3}$
• B. $\frac{\pi}{2}$
• C. $\frac{3\pi}{2}$
• D. $\pi$

Answer 1

Answer: (A)

Since $3sin \,x−4sin ^3x=sin3x$
and $sin3x$ increases when $3x$ takes values from $−\pi/2$ to $\pi/2$ or $x$ takes values from $−\pi/6$ to $\pi/6$.
Thus, the length of the longest interval in which $3sinx − 4sin^3x$ increases is $\pi/6−(−\pi/6)=\pi/3$.