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Question

If x=1 and x=2 are extreme points of f(x)=αlog|x|+βx2+x then :

A
α=6, β=12
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B
α=6, β=12
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C
α=2, β=12
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D
α=2, β=12
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Solution

The correct option is C α=2, β=12
f(x)=αlog|x|+βx2+x
f(x)=αx+2βx+1
At x=1, f(1)=α2β+1=0
At x=2, f(2)=α2+4β+1=0
On solving (1) and (2)
α=2, β=12

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