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  • What is the derivative of   at  <img alt="\mathrm{x=0 \, \, ?}" src=

What is the derivative of \mathrm{f(x)=|x|}  at  \mathrm{x=0 \, \, ?}

Option: 1

1


Option: 2

-1


Option: 3

0


Option: 4

Does not exist


Answers (1)

best_answer

                              \mathrm{f(x)=|x|=\left\{\begin{array}{cc} x, & x>0 \\ -x, & x<0 \end{array}\right.}

\mathrm{\text { Left derivative }=-1}

\mathrm{\text { Right derivative }=+1}

\therefore                          \mathrm{ LD\neq \mathrm{RD}}

 

The derivative does not exist at \mathrm{ x=0 . }

Posted by

Devendra Khairwa

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