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Examine the applicability of Mean Value Theorem for all three functions given in $(ii)\;f (x) = [x] \;for\; x \: \in [-2,2]$

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A)
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  • By Mean value theorem $f'(c)=\large\frac{f(b)-f(a)}{b-a}$
$f(x)=[x]$ for $x\in [-2,2]$.
$f(x)=[x]$ in the interval [-2,2] is neither continuous nor differentiable.Hence Mean Value Theorem is not applicable.
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