In which of the following function is rolle's theorem applicable?

• A. \[f(x)=\left\{ \begin{matrix}    x,\,  \\    0,\,  \\ \end{matrix} \right.\,\begin{matrix}    \,\,\,\,\,0\le x<1  \\    x=1  \\ \end{matrix}\] on [0, 1]
• B. \[f(x)=\left\{ \begin{matrix}    \frac{\sin x}{x},\,  \\    1,\,  \\ \end{matrix} \right.\,\,\,\,\begin{matrix}    -\pi \le x<0  \\    x=0  \\ \end{matrix}\] on [-\[\pi \],0]
• C. \[f(x)=\frac{{{x}^{2}}-x-6}{x-1}\] on [-2, 3]
• D. \[f(x)=\left\{ \begin{matrix}    \frac{{{x}^{3}}-2{{x}^{2}}-5x+6}{x-1},\,\,\,if\,\,x\ne 1,  \\    -\,6,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,x=1  \\ \end{matrix} \right.\]on [-2, 3]