Let $f \in \mathcal { C } ^ { 0 } ( [ 0 , + \infty [ )$ and $\ell \in \mathbb { R }$. Prove that
$$\left( \lim _ { x \rightarrow + \infty } f ( x + 1 ) - f ( x ) = \ell \right) \Rightarrow \left( \lim _ { x \rightarrow + \infty } \frac { f ( x ) } { x } = \ell \right)$$