By means of the function $\psi ( x ) = \sqrt { 1 + x ^ { 2 } }$, show that in the previous question hypothesis (1) cannot be replaced by $$\forall x \in \mathbb { R } , \quad \left| \phi ^ { \prime } ( x ) \right| < 1 .$$
By means of the function $\psi ( x ) = \sqrt { 1 + x ^ { 2 } }$, show that in the previous question hypothesis (1) cannot be replaced by
$$\forall x \in \mathbb { R } , \quad \left| \phi ^ { \prime } ( x ) \right| < 1 .$$