jee-main 2022 Q73

jee-main · India · session1_24jun_shift1 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions

For the function $f ( x ) = 4 \log _ { e } ( x - 1 ) - 2 x ^ { 2 } + 4 x + 5 , x > 1$, which one of the following is NOT correct?
(1) $f ( x )$ is increasing in $( 1,2 )$ and decreasing in $( 2 , \infty )$
(2) $f ( x ) = - 1$ has exactly two solutions
(3) $f ^ { \prime } ( \mathrm { e } ) - f ^ { \prime \prime } ( 2 ) < 0$
(4) $f ( x ) = 0$ has a root in the interval $( e , e + 1 )$

For the function $f ( x ) = 4 \log _ { e } ( x - 1 ) - 2 x ^ { 2 } + 4 x + 5 , x > 1$, which one of the following is NOT correct?\\
(1) $f ( x )$ is increasing in $( 1,2 )$ and decreasing in $( 2 , \infty )$\\
(2) $f ( x ) = - 1$ has exactly two solutions\\
(3) $f ^ { \prime } ( \mathrm { e } ) - f ^ { \prime \prime } ( 2 ) < 0$\\
(4) $f ( x ) = 0$ has a root in the interval $( e , e + 1 )$

Paper Questions

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