If \[f(x)\] is a differentiable function such that \[f:R\to r\] and \[f\left( \frac{1}{n} \right)=0\ \forall \ n\ge 1,n\in I\] then [IIT Screening 2005]

\[f(0)=0\] but \[f'(0)\] may or may not be 0

\[f(x)=0\ \forall \ x\in (0,\,1)\]

\[|f(x)|\,\le 1\ \forall \ x\in (0,\,1)\]

If \[f(x)\] is a differentiable function such that \[f:R\to r\] and \[

1.	If \[f(x)\] is a differentiable function such that \[f:R\to r\] and \[f\left( \frac{1}{n} \right)=0\ \forall \ n\ge 1,n\in I\] then [IIT Screening 2005]
A.	\[f(x)=0\ \forall \ x\in (0,\,1)\]
B.	\[f(x)=0\forall x\in (0,\,1)\]
C.	\[f(0)=0\] but \[f'(0)\] may or may not be 0
D.	\[\|f(x)\|\,\le 1\ \forall \ x\in (0,\,1)\]
Answer» C. \[f(0)=0\] but \[f'(0)\] may or may not be 0

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