jee-main 2014 Q80

jee-main · India · 06apr Stationary points and optimisation Determine parameters from given extremum conditions

If $f$ \& $g$ are differentiable functions in $[ 0,1 ]$ satisfying $f ( 0 ) = 2 = g ( 1 ) , g ( 0 ) = 0$ \& $f ( 1 ) = 6$, then for some $c \in ] 0,1 [$
(1) $f ^ { \prime } ( c ) = g ^ { \prime } ( c )$
(2) $f ^ { \prime } ( c ) = 2 g ^ { \prime } ( c )$
(3) $2 f ^ { \prime } ( c ) = g ^ { \prime } ( c )$
(4) $2 f ^ { \prime } ( c ) = 3 g ^ { \prime } ( c )$

If $f$ \& $g$ are differentiable functions in $[ 0,1 ]$ satisfying $f ( 0 ) = 2 = g ( 1 ) , g ( 0 ) = 0$ \& $f ( 1 ) = 6$, then for some $c \in ] 0,1 [$\\
(1) $f ^ { \prime } ( c ) = g ^ { \prime } ( c )$\\
(2) $f ^ { \prime } ( c ) = 2 g ^ { \prime } ( c )$\\
(3) $2 f ^ { \prime } ( c ) = g ^ { \prime } ( c )$\\
(4) $2 f ^ { \prime } ( c ) = 3 g ^ { \prime } ( c )$

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