Verify Rolles theorem for function `f(x)=cos2x` on `[-pi//4,\ pi//4]`

Explanation

To verify Rolle's Theorem for the function \( f(x) = \cos(2x) \) on the interval \([- \frac{\pi}{4}, \frac{\pi}{4}]\), we need to follow these steps:

### Step 1: Check the conditions of Rolle's Theorem

**Condition 1: Continuity on the closed interval**
The function \( f(x) = \cos(2x) \) is a cosine function, which is continuous everywhere. Therefore, it is continuous on the closed interval \([- \frac{\pi}{4}, \frac{\pi}{4}]\).

**Condition 2: Differentiability on the open interval**
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