Question

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

Answer 1

Correct Answer - 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.