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ISRO-DEC2017-4

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

  1. $\alpha=-6,\beta=\dfrac{-1}{2}$
     
  2. $\alpha=2,\beta=\dfrac{-1}{2}$
     
  3. $\alpha=2,\beta=\dfrac{1}{2}$
     
  4. $\alpha=-6,\beta=\dfrac{1}{2}$
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1 Answer

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Since the extreme points are given ,

d/dx (f(x)) =0
a/x +2bx +1=0
At x=-1,
-a - 2b + 1 = 0
a + 2b = 1 ..........(1)

At x=2,
a/2 + 4b + 1 = 0
a + 8b = -2 ..........(2)
subtracting (1) & (2),
b=-1/2
put value of b in (1)
a=2
hence option (B) is correct
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