Question

When $0$\le x \le 1,$f\left(x\right)=|x|+|x-1|$ is

• A. increasing
• B. decreasing
• C. constant
• D. None of these

Answer 1

The correct option is C constant

$f\left(x\right)=|x|+|x-1|$
For $x<0$
$f\left(x\right)=-x-(x-1)=-2x+1$
For $0\le x\le 1$
$f\left(x\right)=x-(x-1)=1$
For $x>1$
$f\left(x\right)=x+x-1=2x-1$
Hence, $f\left(x\right)=\{\begin{array}{c}-2x+1,x<0\\ 1,0\le x\le 1\\ 2x-1,1<x\end{array}$
$\Rightarrow f^{\prime }\left(x\right)=\{\begin{array}{c}-2,x<0\\ 0,0\le x\le 1\\ 2,1<x\end{array}$
It is constant function at $0\le x\le 1$