At what points in the interval `[0,2pi]`, does the function `sin 2x` attain its maximum value?

Explanation

To determine the points in the interval \([0, 2\pi]\) where the function \( \sin(2x) \) attains its maximum value, we can follow these steps:

### Step 1: Identify the function and its range
The function we are analyzing is \( f(x) = \sin(2x) \). The sine function oscillates between -1 and 1. Therefore, the maximum value of \( \sin(2x) \) is 1.

### Step 2: Set up the equation for maximum value
To find the points where \( f(x) \) attains its maximum value, we need to solve the equation:
\[
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