Question

Let $f\left(x\right)=x^3-x^2+x+1$ and $g\left(x\right)=\{\begin{array}{c}max\left\{f\right(t)for0\le t\le x\}for0\le x\le 1\\ 3-x+x^{2}for1<x\le 2\end{array}$, then

• A. $g\left(x\right)$ is continuous & derivable at $x=1$
• B. $g\left(x\right)$ is continuous but not derivable at $x=1$
• C. $g\left(x\right)$ is neither continuous nor derivable at $x=1$
• D. $g\left(x\right)$ is derivable but not continuous at $x=1$

Answer 1

The correct option is C $g\left(x\right)$ is neither continuous nor derivable at $x=1$