# Cubic polynomials give third degree burns to my brain

Calculus Level 4

Let $\displaystyle f(x)$ be a polynomial of degree $\displaystyle 3$, satisfying $\displaystyle f(3) = 5$ and $\displaystyle f(-1) = 9$.

$\displaystyle f(x)$ has a minimum at $\displaystyle x=0$ and $\displaystyle f'(x)$ has a maximum at $\displaystyle x=1$.

Find the distance between the local maximum and local minimum of $\displaystyle f(x)$.

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