The function f(X)=k sinx +`1/3` sinx 3x has maximum value at `x=(pi)/(3)` what is the value of k?

Options

A. 3
B. `1/3`
C. 2
D. `1/2`

Explanation

To find the value of \( k \) such that the function \( f(x) = k \sin x + \frac{1}{3} \sin 3x \) has a maximum at \( x = \frac{\pi}{3} \), we will follow these steps:

### Step 1: Differentiate the function
We start by differentiating \( f(x) \) with respect to \( x \).

\[ f'(x) = \frac{d}{dx}(k \sin x + \frac{1}{3} \sin 3x) \]
...