I have to find a, b, c, and d such that the function defined by :
f(x) = ax3+bx2+cx+d
will have a relative extrema at points (1,2) and (2,3).
The Attempt at a Solution
From the given critical points, I am able to know that when x=1 or x=2, f'(x)=3ax2+2bx+c should be equal to zero.
Therefore f'(x) should have factors like (x-1) and (x-2) or in simplified form x2-3x+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?