Rise within Roots

Calculus Level 2

\[f(x) = 2x^3 -15x^2 + 36x -27\]

Let \(a\) and \(b\) be the distinct roots of the function above. If \((c , d)\) is the domain, where \(f(x)\) is increasing within \((a , b)\), find \(c\times d\).

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