\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f(x) = x^3-3x^2+x+2\).
  1. Find the second derivative, \(f''(x)\).
  2. Find the x-coordinate of the potential point of inflection.
  3. Use a sign diagram for \(f''(x)\) to show that a point of inflection exists at this x-coordinate.
  4. Find the coordinates of the point of inflection and classify it as stationary or non-stationary.

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