Question

Let $f\left(x\right)=|x-1|+|x+1|$.Then which of the following is true?

• A. $f\left(x\right)$ is differentiable at $x=\pm$ 1
• B. $f\left(x\right)$ is not differentiable at $x=\pm$1
• C. $f\left(x\right)$ is neither continuous nor differentiable at $x=\pm$1
• D. $f\left(x\right)$ is continuous at $x=0$

Answer 1

Answer: (B), (C)

The correct options are
B $f\left(x\right)$ is not differentiable at $x=\pm$1
C $f\left(x\right)$ is neither continuous nor differentiable at $x=\pm$1

$f\left(x\right)=\begin{array}{ccc}2x& x>1& \\ 2& -1\le X\le 1& \\ -2x& x<-1& \end{array}$
$f^{{}^{\prime }}\left(x\right)=\begin{array}{cc}2& x>1\\ 0& -1\le x\le 1\\ -2& x<-1\end{array}$
$f^{{}^{\prime }}\left(x^{-}\right)\ne f^{{}^{\prime }}\left(x^{+}\right)$
$f^{{}^{\prime }}(-1^{-})\ne f^{{}^{\prime }}(-1^{+})$
So f(x) is not differantiable at $x=\pm 1$