jee-main 2022 Q73

jee-main · India · session1_26jun_shift1 Stationary points and optimisation Find absolute extrema on a closed interval or domain

The sum of the absolute minimum and the absolute maximum values of the function $f ( x ) = \left| 3 x - x ^ { 2 } + 2 \right| - x$ in the interval $[ - 1 , 2 ]$ is
(1) $\frac { \sqrt { 17 } + 3 } { 2 }$
(2) $\frac { \sqrt { 17 } + 5 } { 2 }$
(3) 5
(4) $\frac { 9 - \sqrt { 17 } } { 2 }$

The sum of the absolute minimum and the absolute maximum values of the function $f ( x ) = \left| 3 x - x ^ { 2 } + 2 \right| - x$ in the interval $[ - 1 , 2 ]$ is\\
(1) $\frac { \sqrt { 17 } + 3 } { 2 }$\\
(2) $\frac { \sqrt { 17 } + 5 } { 2 }$\\
(3) 5\\
(4) $\frac { 9 - \sqrt { 17 } } { 2 }$

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