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Let $f: D \rightarrow R$ where $D=[0,1] \cup[2,4]$ be defined by $f(x)=\left\{\begin{array}{ll}x, & \text { if } x \in[0,1] \\ 4-x, & \text { if } x \in[2,4]\end{array}\right.$. Then,
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The correct answer is:
Rolle's theorem is not applicable to $\mathrm{f}$ in $\mathrm{D}$
$f(x)=\left\{\begin{array}{ll}x, & x \in[0,1] \\ 4-x, & x \in[2,4]\end{array}\right.$
$f(x)$ is increasing in $[0,1]$
and $f(x)$ is decreasing in $[2,4]$
$\therefore$ Rolle's theorem is not applicable to $\mathrm{f}$ in $\mathrm{D}$.
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