Find the maximum and minimum values of `f(x)=sinx+1/2cos2x` in `[0,\ pi//2]` .

Explanation

To find the maximum and minimum values of the function \( f(x) = \sin x + \frac{1}{2} \cos 2x \) in the interval \([0, \frac{\pi}{2}]\), we will follow these steps:

### Step 1: Find the derivative of the function
First, we need to differentiate \( f(x) \) with respect to \( x \).

\[ f'(x) = \frac{d}{dx}(\sin x) + \frac{1}{2} \frac{d}{dx}(\cos 2x) \]
...