The question goes as follows:
Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$, then $p'(0)$ is...
What I did first, naturally, was consider that $p(x)$ is a cubic. But, all conditions cannot be satisfied simultaneously if $p(x)$ is a cubic.
Next, I considered $p(x)$ to be a $4$ degree polynomial, solved and got $p'(0)=15$. But the answer provided was $p'(0)=9$.