If \[f(x)\] is twice differentiable polynomial function such that \[f(1)=1,f(2)=-4,f(3)=9\], then [IIT Screening 2005]

There exist at least one \[x\in (2,\,3)\] such that \[f'(x)=5=f''(x)\]

There exist at least one \[x\in (1,\,3)\] such that \[f''(x)=2\]

There exist at least one \[x\in (1,\,2)\] such that \[f(x)=3\]

If \[f(x)\] is twice differentiable polynomial function such that \[f(

1.	If \[f(x)\] is twice differentiable polynomial function such that \[f(1)=1,f(2)=-4,f(3)=9\], then [IIT Screening 2005]
A.	\[f''(x)=2,\forall x\in R\]
B.	There exist at least one \[x\in (1,\,3)\] such that \[f''(x)=2\]
C.	There exist at least one \[x\in (2,\,3)\] such that \[f'(x)=5=f''(x)\]
D.	There exist at least one \[x\in (1,\,2)\] such that \[f(x)=3\]
Answer» C. There exist at least one \[x\in (2,\,3)\] such that \[f'(x)=5=f''(x)\]

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If \[f(x)\] is twice differentiable polynomial function such that \[f(1)=1,f(2)=-4,f(3)=9\], then [IIT Screening 2005]

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