Calculus + Algebra = Calgebra!

Calculus Level 4

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

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

Then evaluate : limx1(f(x).f(x))\lim _{x\rightarrow 1}\left ( f^{'}(x) . f^{''}(x)\right )

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