Let \(f: D \rightarrow R\) where \(D=[0,1] \cup[2,4]\) be defined by \(f(x)=\left\{\begin{array}{l}x, \quad \text { if } x \in[0,1] \\ 4-x, \text { if } x \in[2,4]\end{array}\right.\). Then,
(A) Rolle's theorem is applicable to \(\mathrm{f}\) in \(\mathrm{D}\)
(B) Rolle's theorem is not applicable to \(f\) in \(D\)
(C) there exists \(\xi \in\) D for which \(f^{\prime}(\xi)=0\) but Rolle's theorem is not applicable
(D) \(f\) is not continuous in \(D\)
Ans: (B)
