\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f(x) = \frac{1}{12}x^4 - \frac{1}{2}x^3 + x^2\).
  1. Find the first and second derivatives of \(f(x)\).
  2. Find the x-coordinates of the potential points of inflection.
  3. Use a sign diagram for \(f''(x)\) to show that points of inflection exist at these x-coordinates.
  4. Find the coordinates of the points of inflection and classify them as stationary or non-stationary.

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.