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Consider the function $y=|x|$ in the interval $[-1, 1]$. In this interval, the function is

1. continuous and differentiable
2. continuous but not differentiable
3. differentiable but not continuous
4. neither continuous nor differentiable
asked in Calculus | 739 views

$(b)$ $y$ is continuous but not differentiable at $x=0$ as left hand limit will be negative while the right hand limit will be positive but for differentiation, both must be same.
edited

$y = |x| = \begin{Bmatrix} x & x\geqslant 0 \\ -x& x< 0 \end{Bmatrix}$

$y' = \begin{Bmatrix} 1 & x\geqslant 0 \\ -1& x< 0 \end{Bmatrix}$

continuous but not differentiable at x = 0

answer is b) continuous but not differentiable  ....because at x=0 this function is not differentiable

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