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The Rolle’s theorem is not applicable to $f (x) = {\begin{matrix} x, & 0 \leq x \leq 1 \\ 2 - x, & 1 \leq x \leq 2 \end{matrix}$ on $[0, 2]$ because

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$f (x)$ is not continuous

$f (0) \neq f (2)$

$f (x)$ is not differentiable

$f (x)$ is not defined everywhere

answer is D.

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Check Continuity & Differentiability at [0,2]

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