Mathematics - Differentiation Question with Solution | TestHub

$f(x)=f^{\prime }(x)\times f^{\prime \prime \prime }(x)$ is satisfied by only the polynomial of degree 4. Since $f(x)=0$ satisfies $x=1,2,3$ only, it is clear one of the roots is twice repeated. $\Rightarrow f^{\prime }(1)f^{\prime }(2)f^{\prime }(3)=0$.