ISI2015-MMA-73

Question

$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then

• A. $\alpha$ must be $0$
• B. $\alpha$ need not be $0$, but $\mid \alpha \mid <1$
• C. $\alpha >1$
• D. $\alpha < -1$

Comments

A seems to be the most appropriate answer.