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Question

The least value of αϵR for which 4αx2+1x1, for all x > 0, is

A
164
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B
132
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C
127
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D
125
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Solution

The correct option is C 127
Let f(x)=4αx2+1x
For x > 0, fmin=1
f(x)=8αx1x2=0x=12α1/3
fmin=14α(12α1/3)2+2α1/3=1
3α1/3=1 or α=127

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