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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 by Veteran (59.5k points) | 623 views

4 Answers

+10 votes
Best answer
$(b)$ $y$ 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.
answered by Junior (583 points)
edited by
+1 vote

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

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

continuous but not differentiable at x = 0

answered by Loyal (9k points)
0 votes
answer is b) continuous but not differentiable  ....because at x=0 this function is not differentiable
answered by (115 points)


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