jee-main 2022 Q71

jee-main · India · session2_25jul_shift1 Stationary points and optimisation Find absolute extrema on a closed interval or domain

If the absolute maximum value of the function $f(x) = (x ^ { 2 } - 2x + 7) e ^ { (4x ^ { 3 } - 12x ^ { 2 } - 180x + 31)}$ in the interval $[-3,0]$ is $f(\alpha)$, then
(1) $\alpha = 0$
(2) $\alpha = - 3$
(3) $\alpha \in (-1,0)$
(4) $\alpha \in (-3,-1)$

If the absolute maximum value of the function $f(x) = (x ^ { 2 } - 2x + 7) e ^ { (4x ^ { 3 } - 12x ^ { 2 } - 180x + 31)}$ in the interval $[-3,0]$ is $f(\alpha)$, then\\
(1) $\alpha = 0$\\
(2) $\alpha = - 3$\\
(3) $\alpha \in (-1,0)$\\
(4) $\alpha \in (-3,-1)$

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