ISRO | ISRO CS 2017 | Question 4

If x = -1 and x = 2 are extreme points of f(x) = α log |x| + β x² + x then

(A) α = -6, β = -1/2
(B) α = 2, β = -1/2
(C) α = 2, β = 1/2
(D) α = -6, β =1/2

Answer: (B)
Explanation: f(x) = α log |x| + β x² + x
for extreme points f'(x)=0
f'(x)= α/x + 2βx + 1 = 0
for x= -1: -α -2β = -1
for x= 2: α/2 + 4β = -1
from here we can get the value of α=2 and β= -1/2
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