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

f(x) =

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)= should be equal to zero.

Therefore f'(x) should have factors like (x-1) and (x-2) or in simplified form . 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?