A differentiable function $f : \mathbb { R } \rightarrow \mathbb { R }$ satisfies $f ( 1 ) = 2 , f ( 2 ) = 3$ and $f ( 3 ) = 1$. Show that $f ^ { \prime } ( x ) = 0$ for some $x$.
A differentiable function $f : \mathbb { R } \rightarrow \mathbb { R }$ satisfies $f ( 1 ) = 2 , f ( 2 ) = 3$ and $f ( 3 ) = 1$. Show that $f ^ { \prime } ( x ) = 0$ for some $x$.