Question

Let $y=\left|x\right|+|x-2|$. Then $\frac{dy}{dx}$ at $x=2$

• A. is $2$
• B. is $0$
• C. does not exist
• D. none of these

Answer 1

Answer: (C)

does not exist

$y=\left|x\right|+|x-2|y=\{\begin{array}{c}\begin{array}{cc}2-2x& x<0\end{array}\\ \begin{array}{cc}2& 0\le x<2\end{array}\\ \begin{array}{cc}2x-2& x\ge 2\end{array}\end{array}\frac{dy}{dx}=\{\begin{array}{c}\begin{array}{cc}-2& x<0\end{array}\\ \begin{array}{cc}0& 0\le x<2\end{array}\\ \begin{array}{cc}2& x\ge 2\end{array}\end{array}$
Hence $\frac{dy}{dx}$ does not exists at $x=2$