Find the values of x, if any, for which f(x) has local maximum and local minimum when
`f(x)=sinx+cosx, x in [0, 2pi]`

Explanation

To find the values of \( x \) for which \( f(x) = \sin x + \cos x \) has local maximum and local minimum in the interval \( [0, 2\pi] \), we will follow these steps:

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

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