Question

Not sure how to get to the answer and how to write the sign chart they are asking for, could you please help.

Answer 1

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:

`\begin{gathered} (d)/(dx)(\sin4x)=\cos4x*4 \\ =4\cos4x \end{gathered}`

The above equation implies that the derivative is positive when:

`4x\in(0,(\pi)/(2))\cup((3\pi)/(4),2\pi)`

So, we can say that:

`x\in(0,(\pi)/(8))\cup((3\pi)/(8),(\pi)/(2))`

Thus, option C is correct.