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# Examine the applicability of Mean Value Theorem for all three functions given in $(i)\;f (x) = [x] \;for\; x \: \in [5,9]$

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• By Mean value theorem $f'(c)=\large\frac{f(b)-f(a)}{b-a}$
$f(x=[x]$ for $x\in [5,9]$
$f(x)=[x]$ in the interval [5,9] is neither continuous nor differentiable.
Therefore Mean Value Theorem is not applicable.