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For xge 0 , the smallest value of the fu...

For `xge 0` , the smallest value of the function `f(x)=(4x^2+8x+13)/(6(1+x))`, is ________.

Text Solution

Verified by Experts

The correct Answer is:
2
`f(x) = (4x^(2) + 8x + 13)/(6(1 + x))`
`= (4(x + 1)^(2) + 9)/(6(1 + x))`
`= (2)/(3) (x + 1) + (3)/(2(x + 1))`
`ge 2 sqrt((2)/(3).(3)/(2)) = 2`
Therefore, minimum value of f(x) is 2.
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