\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f(x) = \ln(x) - \frac{x^2}{2}\).
  1. Show that \(f'(x) = \frac{(1-x)(1+x)}{x}\).
  2. Draw the sign diagram for \(f'(x)\).
  3. Hence, find the intervals where \(y=f(x)\) is increasing or decreasing.

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