Question

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

• A. $\pi /3$
• B. $\pi /2$
• C. $3\pi /2$
• D. $\pi$

Answer 1

The correct option is A $\pi /3$

Since $3\sin x-4{\sin }^{3}x=\sin 3x$
and $\sin 3x$ 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 $3\sin x-4{\sin }^{3}x$ increases is $\pi /6-(-\pi /6)=\pi /3$.
Ans: A