# When all's unknown

Calculus Level 5

$\large{ f(x) = ax^3 + bx^2 + cx + d}$

The Taylor Series expansion of $$f(x)$$ about $$x= a$$ is

$\frac{d}{6}(x- a)^3 + (3a + b + 2d)(x- a)^2 + (3a^2 + c + 6d)(x - a)$

Determine the product $$abcd$$, where $$a$$, $$b$$, $$c$$, and $$d$$ are distinct, nonzero, coprime (not necessarily pairwise) integers.

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