grandes-ecoles 2022 Q1.3

grandes-ecoles · France · x-ens-maths__pc_cpge Proof True/False Justification
By means of the function $\psi ( x ) = \sqrt { 1 + x ^ { 2 } }$, show that in the previous question hypothesis (1) cannot be replaced by $$\forall x \in \mathbb { R } , \left| \phi ^ { \prime } ( x ) \right| < 1$$
By means of the function $\psi ( x ) = \sqrt { 1 + x ^ { 2 } }$, show that in the previous question hypothesis (1) cannot be replaced by
$$\forall x \in \mathbb { R } , \left| \phi ^ { \prime } ( x ) \right| < 1$$