Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function such that $\lim _{x \rightarrow \infty} \frac{f(x)}{x}=0$. Then

• A

  there exists a real number $m$ such that $\left|f^{\prime}(x)\right| \lt m$ for all $x \in[0, \infty)$
• Correct answer
  B

  $\lim _{x \rightarrow \infty} \frac{|F(x)|}{x^2}=0$ where $F(x)$ is an antiderivative of $f(x)$
• C

  $\lim _{x \rightarrow \infty} f^{\prime}(x)=\infty$
• Correct answer
  D

  $\lim _{x \rightarrow \infty} f^{\prime}(x)=0$ whenever $\lim _{x \rightarrow \infty} f^{\prime}(x)$ exists

Hence, the correct answer is options: 'B', 'D'.