A) constant
B) increasing
C) decreasing
D) None of these
Correct Answer: D
Solution :
Given,\[f(x)=|x|+|x-1|\]and interval\[[-1,2]\] \[f(x)=\left\{ \begin{matrix} -2x+1 & , & -1\le x<0 \\ +1 & , & 0\le x<1 \\ 2x-1 & , & 1\le x\le 2 \\ \end{matrix} \right.\] \[f'(x)=\left\{ \begin{matrix} -2 & , & -1\le x<0 \\ does\text{ }not\text{ }exist & , & x=0 \\ 0 & , & 0<x<1 \\ does\text{ }not\text{ }exist & , & x=1 \\ 2 & , & 1<x\le 2 \\ \end{matrix} \right.\] Hence,\[f(x)\]is decreasing in the interval\[[-1,0[\]and increasing in\[\left] 1,2 \right]\]. ie,\[f(x)\]is neither decreasing nor increasing in the interval\[[-1,2]\].
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