jee-advanced 2005 Q27

jee-advanced · India · screening Proof Existence or properties of extrema via abstract/theoretical argument

27. Let $f$ be twice differentiable function satisfying $f ( 1 ) = 1 , f ( 2 ) = 4 , f ( 3 ) = 9$, then :
(a) $f ^ { \prime } ( x ) = 2 , \forall x \hat { I } ( R )$
(b) $f ^ { \prime } ( x ) = 5 = f ^ { \prime \prime } ( x )$, for some $x \hat { I } ( 1,3 )$
(c) There exists at least one $x \hat { I } ( 1,3 )$ such that $f ^ { \prime } ( x ) = 2$
(d) none of these

The functions $f ( x )$ and $g ( x )$ from $\mathbb { R }$ to $\mathbb { R }$ are defined by

27. Let $f$ be twice differentiable function satisfying $f ( 1 ) = 1 , f ( 2 ) = 4 , f ( 3 ) = 9$, then :\\
(a) $f ^ { \prime } ( x ) = 2 , \forall x \hat { I } ( R )$\\
(b) $f ^ { \prime } ( x ) = 5 = f ^ { \prime \prime } ( x )$, for some $x \hat { I } ( 1,3 )$\\
(c) There exists at least one $x \hat { I } ( 1,3 )$ such that $f ^ { \prime } ( x ) = 2$\\
(d) none of these\\

Paper Questions

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