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**deltaX** I have to find a, b, c, and d such that the function defined by :

f(x) = $\displaystyle ax^3+bx^2+cx+d$

will have a relative extrema at points (1,2) and (2,3).

From the given critical points, I am able to know that when x=1 or x=2, f'(x)=$\displaystyle 3ax^2+2bx+c$ should be equal to zero.

Therefore f'(x) should have factors like (x-1) and (x-2) or in simplified form $\displaystyle x^2-3x+2$. Now my problem is that how should I relate the two equations of f'(x) for me to be able to solve for the said unknowns?