Cubic polynomials give third degree burns to my brain

Calculus Level 4

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

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

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

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