jee-main 2023 Q80

jee-main · India · session1_25jan_shift1 Stationary points and optimisation Find critical points and classify extrema of a given function

Let $x = 2$ be a local minima of the function $f ( x ) = 2 x ^ { 4 } - 18 x ^ { 2 } + 8 x + 12 , x \in ( - 4,4 )$. If $M$ is local maximum value of the function $f$ in $( - 4,4 )$, then $M =$
(1) $12 \sqrt { 6 } - \frac { 33 } { 2 }$
(2) $12 \sqrt { 6 } - \frac { 31 } { 2 }$
(3) $18 \sqrt { 6 } - \frac { 33 } { 2 }$
(4) $18 \sqrt { 6 } - \frac { 31 } { 2 }$

Let $x = 2$ be a local minima of the function $f ( x ) = 2 x ^ { 4 } - 18 x ^ { 2 } + 8 x + 12 , x \in ( - 4,4 )$. If $M$ is local maximum value of the function $f$ in $( - 4,4 )$, then $M =$\\
(1) $12 \sqrt { 6 } - \frac { 33 } { 2 }$\\
(2) $12 \sqrt { 6 } - \frac { 31 } { 2 }$\\
(3) $18 \sqrt { 6 } - \frac { 33 } { 2 }$\\
(4) $18 \sqrt { 6 } - \frac { 31 } { 2 }$

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