To find:
The interval in which the given function is increasing.
Solution:
The function is increasing in the interval where the derivative of the given function is positive.
Differentiate the given function:
[tex]\begin{gathered} \frac{d}{dx}(\sin4x)=\cos4x\times4 \\ =4\cos4x \end{gathered}[/tex]
The above equation implies that the derivative is positive when:
[tex]4x\in(0,\frac{\pi}{2})\cup(\frac{3\pi}{4},2\pi)[/tex]
So, we can say that:
[tex]x\in(0,\frac{\pi}{8})\cup(\frac{3\pi}{8},\frac{\pi}{2})[/tex]
Thus, option C is correct.
