Double Differentiation or Double Trouble?

Calculus Level 3

\[\large \mathcal Y=\dfrac{f''(\alpha)f''(\beta)f''(\gamma)f''(\delta) }{2^3\cdot 6^2\cdot f(3)}\]

Let the zeros of the function \( f(x) = x^4-3x^3-6x^2+9x+6 \) be \(\alpha,\beta,\gamma,\delta\).
Evaluate the expression above.

Clarification: \(f''(x)\) denotes the second derivative of \(f(x)\).


Inspiration.

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