$\begin{array}{l}
y = \sqrt {{x^2} + 1} - mx - 1\\
y' = \frac{x}{{\sqrt {{x^2} + 1} }} - m\\
HS\,dong\,bien\,tren\,R \Leftrightarrow y' \ge 0,\forall x \in R\\
\Leftrightarrow \frac{x}{{\sqrt {{x^2} + 1} }} - m \ge 0,\forall x \in R \Leftrightarrow m \le \frac{x}{{\sqrt {{x^2} + 1} }} = f\left( x \right)\\
Xet\,f\left( x \right) = \frac{x}{{\sqrt {{x^2} + 1} }}\,co\,f'\left( x \right) = \frac{1}{{\sqrt {{x^2} + 1} \left( {{x^2} + 1} \right)}} > 0,\forall x \in R\\
\Rightarrow HS\,f\left( x \right)\,dong\,bien\,tren\,R\\
Ngoai\,ra,\mathop {\lim }\limits_{x \to + \infty } f\left( x \right) = 1,\mathop {\lim }\limits_{x \to - \infty } f\left( x \right) = - 1\,nen\, - 1 < f\left( x \right) < 1\\
\Rightarrow m \le f\left( x \right),\forall x \in R \Leftrightarrow m \le - 1
\end{array}$
