Question

Let $f:(a,b)\to R$ be a differentiable function. Which of the following statements is/are true :

• A. $\underset{x\to a}{lim}f\left(x\right)=\infty ⟹\underset{x\to a}{lim}|f^{\prime }\left(x\right)|=\infty$
• B. $\underset{x\to a}{lim}{f}^{\prime }\left(x\right)=\infty ⟹\underset{x\to a}{lim}f\left(x\right)=\infty$
• C. $\underset{x\to a}{lim}f\left(x\right)=\infty \nRightarrow \underset{x\to a}{lim}|f^{\prime }\left(x\right)|=\infty$
• D. $\underset{x\to a}{lim}{f}^{\prime }\left(x\right)=\infty \nRightarrow \underset{x\to a}{lim}f\left(x\right)=\infty$

Answer 1

Answer: (A)

$\underset{x\to a}{lim}f\left(x\right)=\infty ⟹\underset{x\to a}{lim}|f^{\prime }\left(x\right)|=\infty$

$f:(a,b)\to R$ is differentiable.

If ${lim}_{x\to a}f\left(x\right)=\infty$

$\Rightarrow {lim}_{x\to a}{f}^{\prime }\left(x\right)=\infty$

Hence, the answer is ${lim}_{x\to a}f\left(x\right)=\infty \Rightarrow {lim}_{x\to a}{f}^{\prime }\left(x\right)=\infty$