Rise within Roots

Calculus Level 2

f(x)=2x315x2+36x27f(x) = 2x^3 -15x^2 + 36x -27

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

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