Calculus + Algebra = Calgebra!

Calculus Level 4

Let $f(x)$ be a monic quartic polynomial such that ,

$f(1) = 11$ , $f(2) = 39$ , $f(3) = 123$ , $f(4) = 323$

Then evaluate : $\lim _{x\rightarrow 1}\left ( f^{'}(x) . f^{''}(x)\right )$