jee-main 2014 Q81

jee-main · India · 06apr Stationary points and optimisation Determine parameters from given extremum conditions

If $x = - 1$ and $x = 2$ are extreme points of $f ( x ) = \alpha \log | x | + \beta x ^ { 2 } + x$, then
(1) $\alpha = 2 , \beta = - \frac { 1 } { 2 }$
(2) $\alpha = 2 , \beta = \frac { 1 } { 2 }$
(3) $\alpha = - 6 , \beta = \frac { 1 } { 2 }$
(4) $\alpha = - 6 , \beta = - \frac { 1 } { 2 }$

If $x = - 1$ and $x = 2$ are extreme points of $f ( x ) = \alpha \log | x | + \beta x ^ { 2 } + x$, then\\
(1) $\alpha = 2 , \beta = - \frac { 1 } { 2 }$\\
(2) $\alpha = 2 , \beta = \frac { 1 } { 2 }$\\
(3) $\alpha = - 6 , \beta = \frac { 1 } { 2 }$\\
(4) $\alpha = - 6 , \beta = - \frac { 1 } { 2 }$

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