ISRO-DEC2017-4

Question

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

• A. $\alpha=-6,\beta=\dfrac{-1}{2}$
   
• B. $\alpha=2,\beta=\dfrac{-1}{2}$
   
• C. $\alpha=2,\beta=\dfrac{1}{2}$
   
• D. $\alpha=-6,\beta=\dfrac{1}{2}$

Comments

d/dx (f(x)) =0 at extreme points

a/x +2bx +1=0

At x=-1,

-a - 2b + 1 = 0 ..........(1)

At x=2,

a/2 + 4b + 1 = 0

a + 8b + 2 = 0 ...........(2)

Solving (1) & (2),

a=-6

b=1/2

Option (D)

---

srivivek95

If u solve ur equations then u will get a = 2 and b = -1/2...

Answer 1

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

Comments

For making eq1, on keeping x=-1 shouldn't coefficient of a be 1 instead of (-1) as it's 1/|x|, not 1/x?