Irrational Exuberance

Calculus Level 3

\[ \large{ f(x) = \begin{cases} x^2 , \quad \text{ rational }x \\ x^3 , \quad \text{ irrational }x \\ \end{cases} } \]

Let \(f(x) \) be described as the function above. If \(f(x) \) is continuous at exactly \(p\) points and differentiable at exactly \(q\) points, find \(p+q\).