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## Homework Statement

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

f(x) =

*x*

**a**^{3}+

*x*

**b**^{2}+

*x+*

**c**

**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)=3

**x**

*a*^{2}+2

**x+**

*b***should be equal to zero.**

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