(2) $\quad \because f\left(1^{+}\right)=0, f(1)=1, f(1)=0$
$\therefore f\left(1^{-}\right)>f(1)=f\left(1^{+}\right) \Rightarrow x=1$ is not a point of local maxima.
(3) Domain of $f(x)$ is given by $-1 \leq[x] \leq 1$
${ \Rightarrow x \in [ - 1,2)}$
${ \Rightarrow f(x) = \left\{ {\begin{array}{*{20}{l}}
{0,}&{ - 1 \le x < 0}\\
{x,}&{0 \le x < 1}\\
{0,}&{1 \le x < 2}
\end{array} \Rightarrow f(x) \ge 0} \right.}$
(4) $\quad \because \quad f(x)$ is discontinuous at $x=1.$
$\therefore $ Rolle's theorem is not applicable
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