Discuss the applicability of Rolles theorem for the function `f(x)=[x]` for `-1lt=xlt=1` , where `[x]` denotes the greatest integer not exceeding `x`

Explanation

Given as function is `f(x)=[x],-1

Firstly, check the continuity of the function `f`.


Here in the interval `x \in[-1,1]`, the function has to be right continuous at `x=1` and left continuous at `x=1`


`\Rightarrow \lim _{x arrow 1+} f(x)=\lim _{x arrow 1+}[x]`
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