jee-main 2022 Q71

jee-main · India · session2_28jul_shift2 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions
The function $f ( x ) = x e ^ { x ( 1 - x ) } , x \in R$, is
(1) increasing in $\left( - \frac { 1 } { 2 } , 1 \right)$
(2) decreasing in $\left( \frac { 1 } { 2 } , 2 \right)$
(3) increasing in $\left( - 1 , - \frac { 1 } { 2 } \right)$
(4) decreasing in $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ 
The function $f ( x ) = x e ^ { x ( 1 - x ) } , x \in R$, is\\
(1) increasing in $\left( - \frac { 1 } { 2 } , 1 \right)$\\
(2) decreasing in $\left( \frac { 1 } { 2 } , 2 \right)$\\
(3) increasing in $\left( - 1 , - \frac { 1 } { 2 } \right)$\\
(4) decreasing in $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$
Paper Questions
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