Find the maximum and minimum values of `f(x)=x+sin2x` in the interval `[0,\ 2pi]`

Explanation

To find the maximum and minimum values of the function \( f(x) = x + \sin(2x) \) on the interval \( [0, 2\pi] \), we will follow these steps:

### Step 1: Find the derivative of \( f(x) \)
We start by differentiating the function:
\[ f'(x) = \frac{d}{dx}(x + \sin(2x)) = 1 + 2\cos(2x) \]

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