JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q73

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MathematicsSingle correct+4 / -1Question 73 of 90

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha\log|x|+\beta x^2+x$ then :

\alpha=2,\ \beta=-\dfrac12

\alpha=2,\ \beta=\dfrac12

\alpha=-6,\ \beta=\dfrac12

\alpha=-6,\ \beta=-\dfrac12

Answer and worked solution

Official answer: A

$f'(x)=\dfrac\alpha x+2\beta x+1$ vanishes at $x=-1$ and $x=2$ :
$-\alpha-2\beta+1=0,\qquad\frac\alpha2+4\beta+1=0.$
So $\beta=-\frac12$ and $\alpha=2$ .

Topics:Maxima and minima

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JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 73