Find the maximum and minimum values of `x` + sin`2x` on `[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 the function
We start by differentiating the function \( f(x) \):
\[ f'(x) = \frac{d}{dx}(x) + \frac{d}{dx}(\sin(2x)) = 1 + 2\cos(2x) \]

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