Question

$f\left(x\right)=\left[\begin{array}{ccc}1-x& ,& (0\le x\le 1)\\ x+2& ,& (1<x<2)\\ 4-x& ,& (2\le x\le 4)\end{array}\right]$

Discuss the continuity & differentiability of $y=f\left(x\right)$ for $0\le x\le 4$.

Answer 1

at $x=1$

${lim}_{x\to a^{-}}f\left(x\right)=0;{lim}_{x\to a^{+}}f\left(x\right)=3$

Not continuous

Not Differentiable

at $x=2$

${lim}_{x\to a^{-}}f\left(x\right)=4;{lim}_{x\to a^{+}}f\left(x\right)=2$

Not continuous

Not Differentiable