Question

The length of a longest interval in which the function

3 sin x – 4 sin³ x is increasing is

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

Answer 1

Answer: (A)

$\frac{\pi}{3}$

Answer 2

Since 3 sin x –4 sin³ x = sin 3x and sin 3x increases when 3x takes values from –$\frac{\pi}{2}$ to $\frac{\pi}{2}$ or x takes values from –$\frac{\pi}{6}$to $\frac{\pi}{6}$. Thus, the length of the longest interval in which 3 sin x –4 sin³ x increases is p/6 – (–$\frac{\pi}{6}$) =$\frac{\pi}{3}$