Let the cubic polynomial $f(x) = x^3 - px + q$ have three real roots,where $p > 0$ and $q > 0$. Which of the following is true?

• A
  The cubic has a local minimum at $x = \sqrt{\frac{p}{3}}$ and a local maximum at $x = -\sqrt{\frac{p}{3}}$.
• B
  The cubic has a local minimum at $x = -\sqrt{\frac{p}{3}}$ and a local maximum at $x = \sqrt{\frac{p}{3}}$.
• C
  The cubic has local minima at both $x = -\sqrt{\frac{p}{3}}$ and $x = \sqrt{\frac{p}{3}}$.
• D
  The cubic has local maxima at both $x = \sqrt{\frac{p}{3}}$ and $x = -\sqrt{\frac{p}{3}}$.