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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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Knowledge Check

  • For x ge 0 , the smallest value of funcation f(x) = (4x^(2) + 8x + 13)/(6(1 + x)) is

    A
    `1`
    B
    `2`
    C
    `(25)/(12)`
    D
    `(13)/(6)`

  • The maximum value of the function f(x)= x^(2)+2x^(2)-4x+6 exits at

    A
    x=-2
    B
    x=1
    C
    x=2
    D
    x=-1

  • The maximum value of the function f(x) =x^(3) + 2x^(2) -4x + 6 exists at:

    A
    `x=-2`
    B
    x=1
    C
    x=2
    D
    `x=-1`

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