Prove: $\lim_{x \to \infty} f'(x) = 2$ indicate $\lim_{x \to \infty}f(x) = \infty$ This question is from last year exam in calculus.
In the answers they mentioned more than one way to solve this question.
The method they used is to build a new function but it was a bit complicated.
I would like to get some help.

By L'Hôpital's rule
$$
\mathop {\lim }\limits_{x \to  + \infty } \frac{{f(x)}}{x} = \mathop {\lim }\limits_{x \to  + \infty } \frac{{f'(x)}}{1} = 2.
$$
Thus
$$
\mathop {\lim }\limits_{x \to  + \infty } f(x) = \mathop {\lim }\limits_{x \to  + \infty } x\mathop {\lim }\limits_{x \to  + \infty } \frac{{f(x)}}{x} =  + \infty .
$$
