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The function $f(x)=|x-3|, x \in R$ is: |
differentiable for all $x \in R$ differentiable only at x = 3 no where continuous differentiable for all $x \in R$, except x = 3 |
differentiable for all $x \in R$, except x = 3 |
The correct answer is Option (4) → differentiable for all $x \in R$, except x = 3 $f(x)=|x-3|$ so $f(x)=\left\{\begin{matrix}x-3&x≥3\\3-x&x<3\end{matrix}\right.$ $f'(x)=\left\{\begin{matrix}1&x≥3\\-1&x<3\end{matrix}\right.$ at $x=3$ LHD ≠ RHD otherwise differentiable |
