Verify Rolles theorem for function `f(x)=sin2x` on `[0,\ pi//2]`

Explanation

To verify Rolle's Theorem for the function \( f(x) = \sin(2x) \) on the interval \([0, \frac{\pi}{2}]\), we will follow these steps:

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

1. **Continuity**: The function \( f(x) = \sin(2x) \) must be continuous on the closed interval \([0, \frac{\pi}{2}]\).
- The sine function is continuous everywhere, hence \( f(x) \) is continuous on \([0, \frac{\pi}{2}]\).

2. **Differentiability**: The function \( f(x) \) must be differentiable on the open interval \((0, \frac{\pi}{2})\).
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