Discussion Forum



1)

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


A) $\alpha=-6,\beta=\frac{1}{2}$

B) $\alpha=-6,\beta=-\frac{1}{2}$

C) $\alpha=2,\beta=-\frac{1}{2}$

D) $\alpha=2,\beta=\frac{1}{2}$

Answer:

Option C

Explanation:

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

$f '(x)=\frac{\alpha}{x}+2\beta x+1$

$f '(-1)=-\alpha-2\beta+1=0$            ........(i)

                     [ At extreme point, f '(x0=0]

$f'(2)=\frac{\alpha}{2}+4\beta+1=0$                  .......(ii)

 On solving  Eqs. (i) and (ii) , we get

     $\alpha=2,\beta=-1/2$