Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a nonconstant differentiable function such that $\lim _{x \rightarrow \infty} f(x)=1$ and $\lim _{x \rightarrow \infty} f^{\prime}(x)=\alpha$ for some $\alpha \in \mathbb{R}$. Then

• A

  $\alpha \gt 1$
• B

  $\alpha \lt -1$
• C

  $\alpha \neq 0$ but $|\alpha| \lt 1$
• Correct answer
  D

  $\alpha=0$

Hence, the correct answer is option: 'D'.