question_answer

The function \[f(x)=\left\{ \begin{matrix}    x,if\,\,\,\,\,\,0\le x\le 1  \\    1,if\,\,\,\,\,\,1<x\le 2  \\ \end{matrix} \right.\]   is

A)  Continuous at all \[x,\] \[0\le x\le 2\] and differentiate at all x, except x = 1 in the interval [0, 2]

B)  Continuous and differentiable at all x in [0, 2]

C)  Not continuous at any point in [0, 2]

D)  Not differentiable at any point [0, 2]

E)  None of these