Q8Multiple correct4 Marks1 Dec 2024

Consider the following function: $f(x)=\begin{cases}\frac{\sin x}{x}, & x\ne0,\\ 1, & x=0.\end{cases}$ Which of the following option(s) is/are true about $f(x)$?

A

$f$ is differentiable for all $x\in\mathbb{R}$.

B

$f$ is not differentiable at $x=0$.

C

$f$ is differentiable at $x=0$ and $f'(0)=0$.

D

$f$ is differentiable at $x=0$ and $f'(0)=1$.