If f is a polynomial of degree 3, such that f(0) = f(2) = f(3) = 1 and f(1) = 0, find f(4).
f(4) = 14.
No such polynomial exists under those conditions! Unless my calculations are wrong...
\(-\frac{x^{3}}{2}+\frac{5x^{2}}{2}-3x+1\)
