Q8Multiple correct3 Marks22 Dec 2024

Consider the function $f : \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \begin{cases} x^2 - |x|, & \text{if } x < 0 \\ x^2 - [x], & \text{if } x \ge 0 \end{cases}$. Which of the following option(s) is(are) correct?

A

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

B

$f$ is continuous at $x = 0$.

C

$f$ is differentiable at $x = 1$.

D

$f$ is not continuous at $x = 1$.