Let \[f(x)=\left\{ \begin{align} & {{x}^{\alpha }}\ln x,x>0 \\ & 0,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{align} \right\}\], Rolle?s theorem is applicable to f for \[x\in [0,1]\], if \[\alpha =\] [IIT Screening 2004]

Let \[f(x)=\left\{ \begin{align} & {{x}^{\alpha }}\ln x,x>0 \\ & 0,\,

1.	Let \[f(x)=\left\{ \begin{align} & {{x}^{\alpha }}\ln x,x>0 \\ & 0,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{align} \right\}\], Rolle?s theorem is applicable to f for \[x\in [0,1]\], if \[\alpha =\] [IIT Screening 2004]
A.	-2
B.	-1
C.	0
D.	\[\frac{1}{2}\]
Answer» E.

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Let \[f(x)=\left\{ \begin{align} & {{x}^{\alpha }}\ln x,x>0 \\ & 0,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{align} \right\}\], Rolle?s theorem is applicable to f for \[x\in [0,1]\], if \[\alpha =\] [IIT Screening 2004]

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