If \[f(x)=\left\{ \begin{align} & \,\,\,\,\,\,\,{{e}^{x}};\,\,\,\,x\le 0 \\ & |1-x|;\,\,x>0 \\ \end{align} \right.\], then [Roorkee 1995]

\[f(x)\] is differentiable at \[x=1\]

\[f(x)\] is differentiable at \[x=0\]

\[f(x)\] is continuous at \[x=0\]

\[f(x)\] is continuous at \[x=1\]

If \[f(x)=\left\{ \begin{align} & \,\,\,\,\,\,\,{{e}^{x}};\,\,\,\,x

1.	If \[f(x)=\left\{ \begin{align} & \,\,\,\,\,\,\,{{e}^{x}};\,\,\,\,x\le 0 \\ & \|1-x\|;\,\,x>0 \\ \end{align} \right.\], then [Roorkee 1995]
A.	\[f(x)\] is differentiable at \[x=0\]
B.	\[f(x)\] is continuous at \[x=0\]
C.	\[f(x)\] is differentiable at \[x=1\]
D.	\[f(x)\] is continuous at \[x=1\]
Answer» C. \[f(x)\] is differentiable at \[x=1\]

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If \[f(x)=\left\{ \begin{align} & \,\,\,\,\,\,\,{{e}^{x}};\,\,\,\,x\le 0 \\ & |1-x|;\,\,x>0 \\ \end{align} \right.\], then [Roorkee 1995]

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