Chapter 4.5, Problem 246E

For the following exercises, consider a third-degree polynomial f(x), which has the properties $f\text{'}\left(1\right)=0,f\text{'}\left(3\right)=0$ . Determine whether the following statements are true or false. Justify your answer.

246. $f\left(x\right)=0$ for some $1\le x\le 3$