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The function \(f\) is defined by \(f(x) = e^x \cos(x)\) for \(x \in [0, 2\pi]\).
  1. Find an expression for \(f'(x)\).
  2. Show that \(f''(x) = -2e^x \sin(x)\).
  3. Hence, find the interval(s) where the graph of \(f\) is concave down.

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