# 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 $$p+q$$.

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