Consider a third-degree polynomial $\displaystyle {f{{\left({x}\right)}}}$ , which has the properties $\displaystyle {f}'{\left({1}\right)}={0},{f}'{\left({4}\right)}={0}$ . Determine whether the following
statements are True or False:

1.  $\displaystyle {f{{\left({x}\right)}}}={0}$ for some $\displaystyle {1}\le{x}\le{4}.$ $\displaystyle$ 
   • True
   • False
2.  $\displaystyle {f}{''}{\left({x}\right)}={0}$ for some $\displaystyle {1}\le{x}\le{4}.$  
   • True
   • False
3. There is no absolute maximum at $\displaystyle {x}={1}$ 
   • True
   • False
4. If $\displaystyle {f{{\left({x}\right)}}}$  has three roots, then it has 1 inflection point.  
   • True
   • False
5. If $\displaystyle {f{{\left({x}\right)}}}$  has one inflection point, then it has three real roots.  
   • True
   • False