This is second part of multipart q2

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- Let $f:[a,b]\rightarrow R$ be continuous on [a,b] and differentiable on (a,b).Such that $f(a)=f(b)$ where a and b are some real numbers.Then there exists some $c$ in $(a,b)$ such that $f'(c)=0$

$f(x)=[x]$ for $x\in [-2,2]$

In the interval $[-2,2],f(x)=[x]$ is not continuous and derivable at $x=-1,0,1$.Hence Rolle's theorem is not applicable.

$f'(x)=0$.But f is neither continuous nor differentiable in the interval $[-2,2]$

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