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Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? $ (ii)\;f (x) = [x] \; for\; x \: \in [-2,2]$

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 $[-2,2]$
answered Aug 16, 2013 by sreemathi.v

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