Question

Let $f\left(x\right)=\{\begin{array}{c}\frac{x^2}{2}0<x\le 1\\ 2x^2-3x+31<x<2\end{array}$ then which is correct

• A. $f$ is continuous in $[0,2]$
• B. $f^{\prime }$ is continuous in $[0,2]$
• C. $f\left(x\right)$ is not continuous at $x=1$
• D. ${lim}_{x\to 1^{+}}f\left(x\right)={lim}_{x\to 1^{-}}f\left(x\right)$

Answer 1

Answer: (B), (C)

The correct options are
B $f^{\prime }$ is continuous in $[0,2]$
C $f\left(x\right)$ is not continuous at $x=1$