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5. Continuity and Differentiation
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Given $f (x) =4\,\, - \,\,{\left( {\frac{1}{2}\, - \,x} \right)^{2/3}}\,$ $g (x) = \left\{ \begin{array}{l}\frac{{\tan \,\,[x]}}{x}\,\,\,\,,\,\,x \ne \,0\\1\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,x\, = \,0\end{array} \right.$
$h (x) = \{x\}$ $k (x) = {5^{{{\log }_2}(x\, + \,3)}}$then in $[0, 1]$ Lagranges Mean Value Theorem is $NOT$ applicable to
A
$f, g, h$
B
$h, k$
C
$f, g$
D
$g, h, k$
Solution
$f$ is not differentiable at $x =\frac{1}{2} $
$g$ is not continuous in $[0, 1]$ at $x = 0$
$h$ is not continuous in $[0, 1]$ at $ x = 1$ & $0 $
$k (x) = {(x + 3)^{{{\ln }_2}5}}= (x + 3)^p$ where $2 < p < 3$
Standard 12
Mathematics
